Skip to main content

Math Calculus CALCULUS:EARLY TRANS W/WEB ASSIGN CARD

Suppose that f (4) = 2, g (4) = 5, f '(4) = 6. and g' ( 4 ) = –3. Find h' (4). (a) h(x) = 3f(x) + 8g(x) (b) h(x) = f(x)g(x) (c) h ( x ) = f ( x ) g ( x ) (d) h ( x ) = g ( x ) f ( x ) + g ( x )

Suppose that f (4) = 2, g (4) = 5, f '(4) = 6. and g' ( 4 ) = –3. Find h' (4). (a) h(x) = 3f(x) + 8g(x) (b) h(x) = f(x)g(x) (c) h ( x ) = f ( x ) g ( x ) (d) h ( x ) = g ( x ) f ( x ) + g ( x )

CALCULUS:EARLY TRANS W/WEB ASSIGN CARD

CALCULUS:EARLY TRANS W/WEB ASSIGN CARD

9th Edition

ISBN: 9780357466278

Author: Stewart

Publisher: CENGAGE L

See similar textbooks

Videos

Textbook Question

Chapter 3.2, Problem 46E

Suppose that f(4) = 2, g(4) = 5, f'(4) = 6. and g'(4) = –3. Find h'(4).

(a) h(x) = 3f(x) + 8g(x)

(b) h(x) = f(x)g(x)

(c) h ( x ) = f ( x ) g ( x )

(d) h ( x ) = g ( x ) f ( x ) + g ( x )

Expert Solution & Answer

bartleby

Trending nowThis is a popular solution!

Check out sample textbook solution

Blurred answer

Chapter 3.2, Problem 45E

Chapter 3.2, Problem 47E

Students have asked these similar questions

Use Euler's method to numerically integrate dy dx -2x+12x² - 20x +8.5 from x=0 to x=4 with a step size of 0.5. The initial condition at x=0 is y=1. Recall that the exact solution is given by y = -0.5x+4x³- 10x² + 8.5x+1

Find an equation of the line tangent to the graph of f(x) = (5x-9)(x+4) at (2,6).

Find the point on the graph of the given function at which the slope of the tangent line is the given slope. 2 f(x)=8x²+4x-7; slope of the tangent line = -3

Chapter 3 Solutions

CALCULUS:EARLY TRANS W/WEB ASSIGN CARD

Ch. 3.1 - (a) How is the number e defined? (b) Use a...Ch. 3.1 - (a) Sketch, by hand, the graph of the function...Ch. 3.1 - Differentiate the function. 3. g(x)=4x+7 Ch. 3.1 - Differentiate the function. 4. g(t)=5t+4t2 Ch. 3.1 - Differentiate the function. 5. f(x)=x75x+3 Ch. 3.1 - Differentiate the function. g(x)=74x23x+12 Ch. 3.1 - Differentiate the function. 7. f(t)=2et Ch. 3.1 - Differentiate the function. 8. F(t)=t3+e3 Ch. 3.1 - Differentiate the function. 9. W()=1.83 Ch. 3.1 - Differentiate the function. 10. r(z)=z5z1/2

Ch. 3.1 - Differentiate the function. 11. f(x)=x3/2+x3 Ch. 3.1 - Differentiate the function. 12. V(t)=t3/5+t4 Ch. 3.1 - Differentiate the function. 13. s(t)=1t+1t2 Ch. 3.1 - Differentiate the function. 14. r(t)=at2+bt4 Ch. 3.1 - Differentiate the function. 15. ] y=2x+x Ch. 3.1 - Differentiate the function. 16. h(w)=2w2 Ch. 3.1 - Differentiate the function. 17. g(x)=1x+x4 Ch. 3.1 - Differentiate the function. 18. W(t)=t2et Ch. 3.1 - Differentiate the function. 19. f(x)=x3(x+3)Ch. 3.1 - Differentiate the function. 20. F(t)=(2t3)2 Ch. 3.1 - Differentiate the function. 21. y=3ex+4x3 Ch. 3.1 - Prob. 22E Ch. 3.1 - Differentiate the function. 23. f(x)=3x2+x3x Ch. 3.1 - Differentiate the function. 24. y=x+xx2 Ch. 3.1 - Differentiate the function. 25. G(r)=3r3/2+r5/2r Ch. 3.1 - Differentiate the function. 26. G(t)=5t+7t Ch. 3.1 - Differentiate the function. 27. j(x)=x2.4+e2.4 Ch. 3.1 - Differentiate the function. 28. k(r)=er+re Ch. 3.1 - Differentiate the function. 29. F(z)=A+Bz+Cz2z2 Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Differentiate the function. 32. f()=32ev Ch. 3.1 - Differentiate the function. 33. P(w)=2w2w+4w Ch. 3.1 - Differentiate the function. y = ex + 1 + 1 Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find equations of the tangent line and normal line...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find f'(x). Compare the graphs of f and f' and use...Ch. 3.1 - Find f'(x). Compare the graphs of f and f' and use...Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Find the first and second derivatives of the...Ch. 3.1 - Find the first and second derivatives of the...Ch. 3.1 - Find the first and second derivatives of the...Ch. 3.1 - Find the first and second derivatives of the...Ch. 3.1 - The equation of motion of a particle is s = t3 ...Ch. 3.1 - The equation of motion of a particle is s = t4 ...Ch. 3.1 - Biologists have proposed a cubic polynomial to...Ch. 3.1 - The number of tree species S in a given area A in...Ch. 3.1 - Boyles Law states that when a sample of gas is...Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - For what value of x does the graph of f(x) = ex ...Ch. 3.1 - Show that the curve y = 2ex + 3x + 5x3 has no...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find equations of both lines that are tangent to...Ch. 3.1 - At what point on the curve y = 1 + 2ex 3x is the...Ch. 3.1 - Find an equation of the normal line to the curve...Ch. 3.1 - Where does the normal line to the parabola y = x2 ...Ch. 3.1 - Draw a diagram to show that there are two tangent...Ch. 3.1 - (a) Find equations of both lines through the point...Ch. 3.1 - Use the definition of a derivative to show that if...Ch. 3.1 - Find the nth derivative of each function by...Ch. 3.1 - Find a second-degree polynomial P such that P(2) =...Ch. 3.1 - The equation y" + y' 2y = x2 is called a...Ch. 3.1 - Find a cubic function y = ax3 + bx2 + cx + d whose...Ch. 3.1 - Find a parabola with equation y = ax2 + bx + c...Ch. 3.1 - Let {x2+1ifx1x+1ifx1 Is f differentiable at 1?...Ch. 3.1 - At what numbers is the following function g...Ch. 3.1 - (a) For what values of x is the function f(x) =...Ch. 3.1 - Where is the function h(x) = |x 1| + |x + 2|...Ch. 3.1 - Find the parabola with equation y = ax2 + bx whose...Ch. 3.1 - Suppose the curve y = x4 + ax3 + bx2 + cx + d has...Ch. 3.1 - For what values of a and b is the line 2x + y = b...Ch. 3.1 - Prob. 82E Ch. 3.1 - What is the value of c such that the line y = 2x +...Ch. 3.1 - The graph of any quadratic function f(x) = ax2 +...Ch. 3.1 - Let f(x){x2ifx2mx+bifx2 Find the values of m and b...Ch. 3.1 - Find numbers a and b such that the given function...Ch. 3.1 - Prob. 87E Ch. 3.1 - Prob. 88E Ch. 3.1 - Prob. 89E Ch. 3.1 - Prob. 90E Ch. 3.1 - If c12, how many lines through the point (0, c)...Ch. 3.1 - Prob. 1AP Ch. 3.2 - Find the derivative of f(x) = (1 + 2x2)(x x2) in...Ch. 3.2 - Find the derivative o f the function...Ch. 3.2 - Differentiate. 3. y=4x2+3(2x+5)Ch. 3.2 - Differentiate. 4. y=10x2+7x22x2 Ch. 3.2 - Differentiate. 5. y=x3ex Ch. 3.2 - Differentiate. 6. y=ex+22ex1 Ch. 3.2 - Differentiate. 7. f(x)=3x25xex Ch. 3.2 - Differentiate. 8. g(x)=(x+2x)ex Ch. 3.2 - Differentiate. 9. y=xex Ch. 3.2 - Prob. 10E Ch. 3.2 - Differentiate. 11. g(t)=32t5t+1 Ch. 3.2 - Differentiate. 12. G(u)=6u45uu+1 Ch. 3.2 - Differentiate. 13. f(t)=5tt3t1 Ch. 3.2 - Prob. 14E Ch. 3.2 - Differentiate. 15. y=sss2 Ch. 3.2 - Differentiate. 16. y=xx+1 Ch. 3.2 - Differentiate. 17. J(u)=1u+1u2u+1u Ch. 3.2 - Prob. 18E Ch. 3.2 - Differentiate. 19. H(u)=(uu)(u+u)Ch. 3.2 - Prob. 20E Ch. 3.2 - Differentiate. 21. V(t)=t+2ett Ch. 3.2 - Prob. 22E Ch. 3.2 - Differentiate. 23. y=ep(p+pp)Ch. 3.2 - Differentiate. f(t)=t3t3 Ch. 3.2 - Differentiate. 26. y=z2+ezz Ch. 3.2 - Differentiate. f(x)=x2exx2+ex Ch. 3.2 - Prob. 28E Ch. 3.2 - Differentiate. f(x)=xx+cx Ch. 3.2 - Differentiate. f(x)=ax+bcx+d Ch. 3.2 - Find f'(x) and f"(x). f(x)=xex Ch. 3.2 - Find an equation of the tangent line to the given...Ch. 3.2 - (a) The curve y = 1/(1 + x2) is called a witch of...Ch. 3.2 - (a) The curve y = x/(1 + x2) is called a...Ch. 3.2 - (a) If f(x) = (x3 x)ex, find f'(x). (b) Check to...Ch. 3.2 - (a) If f(x) = (x2 1)/(x2 + 1), find f'(x) and...Ch. 3.2 - If f(x) = x2/(l + x), find f"(1).Ch. 3.2 - If g(x) = x/ex. find g(n)(x).Ch. 3.2 - Suppose that f(5) = 1, f'(5) = 6, g(5) = 3, and...Ch. 3.2 - Suppose that f(4) = 2, g(4) = 5, f'(4) = 6. and...Ch. 3.2 - If f(x) = exg(x), where g(0) = 2 and g'(0) = 5,...Ch. 3.2 - If h(2) = 4 and h'(2) = 3, find ddx(h(x)x)|x=2 Ch. 3.2 - If g(x) = xf(x), where f(3) = 4 and f'(3) = 2,...Ch. 3.2 - If f(2) = 10 and f'(x) = x2f(x) for all x, find...Ch. 3.2 - If f and g are the functions whose graphs are...Ch. 3.2 - Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F...Ch. 3.2 - If g is a differentiable function, find an...Ch. 3.2 - If f is a differentiable function, find an...Ch. 3.2 - How many tangent lines to the curve y = x/(x + 1)...Ch. 3.2 - Find equations of the tangent lines to the curve...Ch. 3.2 - Find R'(0), where R(x)=x3x3+5x51+3x3+6x6+9x9 Hint:...Ch. 3.2 - Prob. 58E Ch. 3.2 - A manufacturer produces bolts of a fabric with a...Ch. 3.2 - The Michaelis-Menten equation for the enzyme...Ch. 3.2 - Prob. 62E Ch. 3.2 - Extended Product Rule The Product Rule can be...Ch. 3.2 - (a) If F(x) = f(x) g(x), where f and g have...Ch. 3.2 - Prob. 65E Ch. 3.2 - Prob. 66E Ch. 3.3 - Differentiate. 1. f(x)=3sinx2cosx Ch. 3.3 - Differentiate. 2. f(x)=tanx4sinx Ch. 3.3 - Differentiate. 3. y=x2+cotx Ch. 3.3 - Differentiate. y = 2 sec x csc x Ch. 3.3 - Prob. 5E Ch. 3.3 - Differentiate. 6. g(x)=3x+x2cosx Ch. 3.3 - Differentiate. y = sec tan Ch. 3.3 - Differentiate. y = sin cos Ch. 3.3 - Differentiate. 9. f()=(cos)sin Ch. 3.3 - Differentiate. g() = e(tan )Ch. 3.3 - Differentiate. 11. H(t)=cos2t Ch. 3.3 - Differentiate. 12. f(x)=exsinx+cosx Ch. 3.3 - Differentiate f()=sin1+cos Ch. 3.3 - Differentiate. y=cosx1sinx Ch. 3.3 - Differentiate. 15. y=x2tanx Ch. 3.3 - Differentiate. f(t)=cottet Ch. 3.3 - Differentiate. 17. f(w)=1+secw1secw Ch. 3.3 - Differentiate. y=sint1+tant Ch. 3.3 - Differentiate. y=tsint1+t Ch. 3.3 - Prob. 20E Ch. 3.3 - Differentiate. f() = cos sin Ch. 3.3 - Differentiate. f(t) = tet cot t Ch. 3.3 - Show that ddx(cscx)=cscxcotx .Ch. 3.3 - Show that ddx(secx)=secxtanx .Ch. 3.3 - Show that ddx(cotx)=csc2x .Ch. 3.3 - Prove, using the definition of a derivative, that...Ch. 3.3 - Find an equation of the tangent line to the curve...Ch. 3.3 - Prob. 29E Ch. 3.3 - (a) Find an equation of the tangent line to the...Ch. 3.3 - Prob. 32E Ch. 3.3 - (a) If f(x) = sec x x, find f'(x). (b) Check to...Ch. 3.3 - (a) If f(x) = ex cos x, find f'(x) and f"(x). (b)...Ch. 3.3 - If f(t) = sec t, find f"(/4).Ch. 3.3 - (a) Use the Quotient Rule to differentiate the...Ch. 3.3 - Suppose f(/3) = 4 and f'(/3) = 2, and let g(x) =...Ch. 3.3 - For what values of x does the graph of f have a...Ch. 3.3 - For what values of x does the graph of f have a...Ch. 3.3 - A mass on a spring vibrates horizontally on a...Ch. 3.3 - An elastic band is hung on a hook and a mass is...Ch. 3.3 - A ladder 10 ft long rests against a vertical wall....Ch. 3.3 - An object with weight W is dragged along a...Ch. 3.3 - Find the limit. limx0sin5x3x Ch. 3.3 - Find the limit. limx0sinxsinx Ch. 3.3 - Prob. 53E Ch. 3.3 - Find the limit. limx0sin3xsin5xx2 Ch. 3.3 - Prob. 55E Ch. 3.3 - Find the limit. limx0cscxsin(sinx)Ch. 3.3 - Prob. 57E Ch. 3.3 - Find the limit. limx0sin(x2)x Ch. 3.3 - Prob. 59E Ch. 3.3 - Prob. 60E Ch. 3.3 - Find the given derivative by finding the first few...Ch. 3.3 - Find the given derivative by finding the first few...Ch. 3.3 - Find constants A and B such that the function y =...Ch. 3.3 - (a) Evaluate limxxsin1x. (b) Evaluate limx0xsin1x....Ch. 3.3 - Differentiate each trigonometric identity to...Ch. 3.3 - A semicircle with diameter PQ sits on an isosceles...Ch. 3.3 - The figure shows a circular arc of length s and a...Ch. 3.3 - Prob. 68E Ch. 3.4 - Write the composite function in the form f(g(x)) ....Ch. 3.4 - Prob. 2E Ch. 3.4 - Write the composite function in the form f(g(x)) ....Ch. 3.4 - Write the composite function in the form f(g(x)) ....Ch. 3.4 - Write the composite function in the form f(g(x))....Ch. 3.4 - Write the composite function in the form f(g(x)) ....Ch. 3.4 - Find the derivative of the function. 7....Ch. 3.4 - Find the derivative of the function. 8....Ch. 3.4 - Find the derivative of the function. f(x)=5x+1 Ch. 3.4 - Find the derivative of the function. f(x)=1x213 Ch. 3.4 - Find the derivative of the function. 11....Ch. 3.4 - Prob. 12E Ch. 3.4 - Find the derivative of the function. f() = cos(2)Ch. 3.4 - Find the derivative of the function. g() = cos2 Ch. 3.4 - Find the derivative of the function. 15. g(x)=ex2x Ch. 3.4 - Find the derivative of the function. 16. y=5x Ch. 3.4 - Find the derivative of the function. y = x2e3x Ch. 3.4 - Find the derivative of the function. f(t) = t sin ...Ch. 3.4 - Find the derivative of the function. f(t) = eat...Ch. 3.4 - Find the derivative of the function. 21....Ch. 3.4 - Find the derivative of the function. 22....Ch. 3.4 - Find the derivative of the function. y=xx+1 Ch. 3.4 - Find the derivative of the function. y=(x+1x)5 Ch. 3.4 - Find the derivative of the function. y = e tan Ch. 3.4 - Find the derivative of the function. f(t)2t3 Ch. 3.4 - Find the derivative of the function....Ch. 3.4 - Find the derivative of the function....Ch. 3.4 - Find the derivative of the function. r(t)=10t2 Ch. 3.4 - Find the derivative of the function. f(z) =...Ch. 3.4 - Find the derivative of the function....Ch. 3.4 - Find the derivative of the function. J() = tan2(n)Ch. 3.4 - Find the derivative of the function. F(t) = et sin...Ch. 3.4 - Find the derivative of the function. F(t)=t2t3+1 Ch. 3.4 - Find the derivative of the function. G(x) = 4C/x Ch. 3.4 - Prob. 36E Ch. 3.4 - Prob. 37E Ch. 3.4 - Prob. 38E Ch. 3.4 - Find the derivative of the function. 39....Ch. 3.4 - Prob. 40E Ch. 3.4 - Find the derivative of the function. 41. y= sin 2...Ch. 3.4 - Find the derivative of the function. y = esin 2x +...Ch. 3.4 - Find the derivative of the function. 43....Ch. 3.4 - Find the derivative of the function. 44....Ch. 3.4 - Find the derivative of the function. f(t) =...Ch. 3.4 - Find the derivative of the function. y=x+x+x Ch. 3.4 - Find the derivative of the function. 47....Ch. 3.4 - Find the derivative of the function. y=234x Ch. 3.4 - Find the derivative of the function. 49....Ch. 3.4 - Find the derivative of the function. 50....Ch. 3.4 - Find the derivative of the function....Ch. 3.4 - Find the derivative of the function. 52....Ch. 3.4 - Find y and y. y = cos(sin 3)Ch. 3.4 - Find y and y . 54. y=(1+x)3 Ch. 3.4 - Find y and y. y=eex Ch. 3.4 - Find an equation of the tangent line to the curve...Ch. 3.4 - Find an equation of the tangent line to the curve...Ch. 3.4 - Find an equation of the tangent line to the curve...Ch. 3.4 - Find an equation of the tangent line to the curve...Ch. 3.4 - Prob. 61E Ch. 3.4 - (a) The curve y=|x|/2x2 is called a bullet-nose...Ch. 3.4 - (a) If f(x)=2x2x, find f(x). (b) Check to see that...Ch. 3.4 - Prob. 64E Ch. 3.4 - Find all points on the graph of the function f(x)...Ch. 3.4 - At what point on the curve y=1+2x is the tangent...Ch. 3.4 - If F(x) = f(g(x)), where f(2) = 8, f(2) = 4, f(5)...Ch. 3.4 - If h(x)=4+3f(x), where f(1) = 7andf(1) = 4, find...Ch. 3.4 - A table of values for f, g, f, and g is given. (a)...Ch. 3.4 - Let f and g be the functions in Exercise 69. (a)...Ch. 3.4 - If f and g are the functions whose graphs are...Ch. 3.4 - If f is the function whose graph is shown, let...Ch. 3.4 - If g(x)=f(x), where the graph off is shown,...Ch. 3.4 - Prob. 74E Ch. 3.4 - Suppose f is differentiable on . Let F(x) = f(ex)...Ch. 3.4 - Let g(x) = ecx + f(x) and h(x) = ekxf(x), where...Ch. 3.4 - Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3,...Ch. 3.4 - If g is a twice differentiable function and f(x) =...Ch. 3.4 - Prob. 79E Ch. 3.4 - Prob. 80E Ch. 3.4 - Show that the function y = e2x (A cos 3x + B sin...Ch. 3.4 - For what values of r does the function y = erx...Ch. 3.4 - Find the 50th derivative of y = cos 2x.Ch. 3.4 - Prob. 84E Ch. 3.4 - The displacement of a particle on a vibrating...Ch. 3.4 - If the equation of motion of a particle is given...Ch. 3.4 - A Cepheid variable star is a star whose brightness...Ch. 3.4 - In Example 1.3.4 we arrived at a model for the...Ch. 3.4 - Prob. 89E Ch. 3.4 - Under certain circumstance a rumor spreads...Ch. 3.4 - The average blood alcohol concentration (BAC) of...Ch. 3.4 - Air is being pumped into a spherical weather...Ch. 3.4 - Prob. 93E Ch. 3.4 - Prob. 94E Ch. 3.4 - Use the Chain Rule to prove the following. (a) The...Ch. 3.4 - Prob. 96E Ch. 3.4 - Use the Chain Rule to show that if is measured in...Ch. 3.4 - Prob. 98E Ch. 3.4 - Prob. 99E Ch. 3.4 - Prob. 101E Ch. 3.4 - Prob. 102E Ch. 3.4 - An approach path for an aircraft landing is shown...Ch. 3.4 - Prob. 2AP Ch. 3.4 - Prob. 3AP Ch. 3.5 - (a) Find y by implicit differentiation. (b) Solve...Ch. 3.5 - (a) Find y by implicit differentiation. (b) Solve...Ch. 3.5 - (a) Find y by implicit differentiation. (b) Solve...Ch. 3.5 - (a) Find y by implicit differentiation. (b) Solve...Ch. 3.5 - Find dy/dx by implicit differentiation. 5. x2 4xy...Ch. 3.5 - Find dy/dx by implicit differentiation. 6. 2x2 +...Ch. 3.5 - Find dy/dx by implicit differentiation. 7. x4 +...Ch. 3.5 - Find dy/dx by implicit differentiation. 8. x3 xy2...Ch. 3.5 - Find dy/dx by implicit differentiation. 9....Ch. 3.5 - Find dy/dx by implicit differentiation. 10. xey =...Ch. 3.5 - Find dy/dx by implicit differentiation. 11. y cos...Ch. 3.5 - Find dy/dx by implicit differentiation. 13....Ch. 3.5 - Find dy/dx by implicit differentiation. 16....Ch. 3.5 - Find dy/dx by implicit differentiation. 15. ex/y...Ch. 3.5 - If f(x) + x2 [f(x)]3 = 10 and f(1) = 2, find f(1).Ch. 3.5 - If g(x) + x sin g(x) = x2, find g(0).Ch. 3.5 - Regard y as the independent variable and x as the...Ch. 3.5 - Regard y as the independent variable and x as the...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Prob. 28E Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Prob. 34E Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - (a) The curve with equation y2 = 5x4 x2 is called...Ch. 3.5 - (a) The curve with equation y2 = x3 + 3x2 is...Ch. 3.5 - Find y by implicit differentiation. 35. x2 + 4y2 =...Ch. 3.5 - Find y by implicit differentiation. 36. x2 + xy +...Ch. 3.5 - Find y by implicit differentiation. 37. sin y +...Ch. 3.5 - Find y by implicit differentiation. 38. x3 y3 = 7 Ch. 3.5 - If xy + ey = e, find the value of y at the point...Ch. 3.5 - If x2 + xy + y3 = 1, find the value of y at the...Ch. 3.5 - Prob. 45E Ch. 3.5 - (a) The curve with equation 2y3+y2y5=x42x3+x2 has...Ch. 3.5 - Find the points on the lemniscate in Exercise 31...Ch. 3.5 - Show by implicit differentiation that the tangent...Ch. 3.5 - Find an equation of the tangent line to the...Ch. 3.5 - Show that the sum of the x-and y-intercepts of any...Ch. 3.5 - Show, using implicit differentiation, that any...Ch. 3.5 - The Power Rule can be proved using implicit...Ch. 3.5 - Prob. 53E Ch. 3.5 - Orthogonal Trajectories Two curves are orthogonal...Ch. 3.5 - Prob. 55E Ch. 3.5 - Orthogonal Trajectories Two curves are orthogonal...Ch. 3.5 - Show that the ellipse x2/a2 + y2/b2 = 1 and the...Ch. 3.5 - Prob. 58E Ch. 3.5 - (a) The van der Waals equation for n moles of a...Ch. 3.5 - The equation x2 xy + y2 = 3 re presents a...Ch. 3.5 - (a) Where does the normal line to the ellipse x2 ...Ch. 3.5 - Find all points on the curve x2y2 + xy = 2 where...Ch. 3.5 - Find equations of both the tangent lines to the...Ch. 3.5 - Use implicit differentiation to find dy/dx for the...Ch. 3.5 - Prob. 66E Ch. 3.5 - The figure shows a lamp located three units to the...Ch. 3.5 - Prob. 1DP Ch. 3.6 - Explain why the natural logarithmic function y =...Ch. 3.6 - Prob. 2E Ch. 3.6 - Differentiate the function. 3. f(x)=lnx2+3x+5 Ch. 3.6 - Differentiate the function. 4. f(x)=xlnxx Ch. 3.6 - Differentiate the function. f(x ) = sin(ln x)Ch. 3.6 - Differentiate the function. f(x) = ln(sin2x)Ch. 3.6 - Differentiate the function. f(x)=ln1x Ch. 3.6 - Differentiate the function. y=1lnx Ch. 3.6 - Differentiate the function. g(x) = ln(xe2x)Ch. 3.6 - Differentiate the function. g(t)=1+lnt Ch. 3.6 - Differentiate the function. F(t) =(ln t)2 sin t Ch. 3.6 - Differentiate the function. 12. p(t)=lnt2+1 Ch. 3.6 - Differentiate the function. 13. y=log8x2+3x Ch. 3.6 - Prob. 14E Ch. 3.6 - Differentiate the function. F(s) = ln ln s Ch. 3.6 - Differentiate the function. p(v)=lnv1v Ch. 3.6 - Differentiate the function. T(z) = 2z log2z Ch. 3.6 - Differentiate the function. 18. g(t)=lntt2+142t13 Ch. 3.6 - Differentiate the function. y = ln(csc x cot x)Ch. 3.6 - Differentiate the function. 21. y=lnex+xex Ch. 3.6 - Prob. 22E Ch. 3.6 - Differentiate the function. 23. h(x)=ex2+lnx Ch. 3.6 - Differentiate the function. 24. y=ln1+2x12x Ch. 3.6 - Differentiate the function. y = log2 (x log5 x)Ch. 3.6 - Show that ddxlnx+x2+1=1x2+1 .Ch. 3.6 - Show that ddxln1cosx1+cosx=cscx .Ch. 3.6 - Find y and y. y=xlnx Ch. 3.6 - Find y and y. y=lnx1+lnx Ch. 3.6 - Find y and y. y = ln |sec x|Ch. 3.6 - Find y and y. y = ln(l + ln x)Ch. 3.6 - Differentiate f and find the domain of f....Ch. 3.6 - Differentiate f and find the domain of f....Ch. 3.6 - Differentiate f and find the domain of f. f(x) =...Ch. 3.6 - Differentiate f and find the domain of f. f(x) ln...Ch. 3.6 - If f(x) = ln(x + ln x), find f(1).Ch. 3.6 - If f(x) = cos(ln x2), find f(1).Ch. 3.6 - Find an equation of the tangent line to the curve...Ch. 3.6 - Find an equation of the tangent line to the curve...Ch. 3.6 - If f(x) = sin x + ln x, find f(x). Check that your...Ch. 3.6 - Find equations of the tangent lines to the curve y...Ch. 3.6 - Let f(x) = cx + ln(cos x). For what value of c is...Ch. 3.6 - Let f(x) = logb (3x2 2). For what value of b is...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Find y if y = ln(x2 + y2).Ch. 3.6 - Find y if xy = yx.Ch. 3.6 - Find a formula for f(n)(x) if f(x) = ln(x 1).Ch. 3.6 - Find d9dx9(x8lnx).Ch. 3.6 - Use the definition of derivative to prove that...Ch. 3.6 - Show that limn(1+xn)n=exfor any x 0.Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Prob. 73E Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Prob. 76E Ch. 3.6 - Find the derivative of the function. Simplify...Ch. 3.6 - Prob. 78E Ch. 3.6 - Prob. 79E Ch. 3.6 - Prob. 80E Ch. 3.6 - Prob. 81E Ch. 3.6 - (a) One way of defining sec1x is to say that...Ch. 3.6 - Use the formula in Exercise 83. 84. If f(4)=5 and...Ch. 3.6 - Use the formula in Exercise 83. 84. If f(4)=5 and...Ch. 3.6 - Use the formula in Exercise 83. 85. If f(x)=x+ex ,...Ch. 3.6 - Prob. 86E Ch. 3.6 - Prob. 87E Ch. 3.6 - Prob. 88E Ch. 3.7 - A particle moves according to a law of motion...Ch. 3.7 - A particle moves according to a law of motion s =...Ch. 3.7 - A particle moves according to a law of motion s =...Ch. 3.7 - A particle moves according to a law of motion s =...Ch. 3.7 - Graphs of the velocity functions of two particles...Ch. 3.7 - Prob. 6E Ch. 3.7 - Prob. 7E Ch. 3.7 - The height (in meters) of a projectile shot...Ch. 3.7 - If a ball is thrown vertically upward with a...Ch. 3.7 - If a rock is thrown vertically upward from the...Ch. 3.7 - A particle moves with position function s = t4 ...Ch. 3.7 - (a) A company makes computer chips from square...Ch. 3.7 - (a) Sodium chlorate crystals are easy to grow in...Ch. 3.7 - (a) Find the average rate of change of the area of...Ch. 3.7 - A stone is dropped into a lake, creating a...Ch. 3.7 - A spherical balloon is being inflated. Find the...Ch. 3.7 - (a) The volume of a growing spherical cell is...Ch. 3.7 - The mass of the part of a metal rod that lies...Ch. 3.7 - The quantity of charge Q in coulombs (C) that has...Ch. 3.7 - Newtons Law of Gravitation says that the magnitude...Ch. 3.7 - Prob. 23E Ch. 3.7 - Some of the highest tides in the world occur in...Ch. 3.7 - Boyles Law states that when a sample of gas is...Ch. 3.7 - If, in Example 4, one molecule of the product C is...Ch. 3.7 - In Example 6 we considered a bacteria population...Ch. 3.7 - The number of yeast cells in a laboratory culture...Ch. 3.7 - Prob. 29E Ch. 3.7 - Prob. 30E Ch. 3.7 - Prob. 31E Ch. 3.7 - Prob. 32E Ch. 3.7 - Prob. 33E Ch. 3.7 - The cost function for a certain commodity is C(q)...Ch. 3.7 - Prob. 35E Ch. 3.7 - If R denotes the reaction of the body to some...Ch. 3.7 - Patients undergo dialysis treatment to remove urea...Ch. 3.7 - Invasive species often display a wave of advance...Ch. 3.7 - The gas law for an ideal gas at absolute...Ch. 3.7 - In a fish farm, a population of fish is introduced...Ch. 3.7 - In the study of ecosystems, predator-prey models...Ch. 3.7 - Prob. 43E Ch. 3.8 - A population of the yeast cell Saccharomyces...Ch. 3.8 - A common inhabitant of human intestines is the...Ch. 3.8 - A culture of the bacterium Salmonella enteritidis...Ch. 3.8 - A bacteria culture grows with constant relative...Ch. 3.8 - The table gives estimates of the world population,...Ch. 3.8 - Experiments show that if the chemical reaction...Ch. 3.8 - Strontium-90 has a half-life of 28 days. (a) A...Ch. 3.8 - The half-life of cesium-137 is 30 years. Suppose...Ch. 3.8 - A sample oflritium-3 decayed to 94.5% of its...Ch. 3.8 - Prob. 11E Ch. 3.8 - Radiocarbon Dating Scientists can determine the...Ch. 3.8 - Prob. 13E Ch. 3.8 - A curve passes through the point (0, 5) and has...Ch. 3.8 - A roast turkey is taken from an oven when its...Ch. 3.8 - In a murder investigation, the temperature of the...Ch. 3.8 - When a cold drink is taken from a refrigerator,...Ch. 3.8 - A freshly brewed cup of coffee has temperature 95C...Ch. 3.8 - Prob. 19E Ch. 3.8 - Prob. 20E Ch. 3.8 - Prob. 21E Ch. 3.8 - Prob. 22E Ch. 3.9 - (a) If V is the volume of a cube with edge length...Ch. 3.9 - (a) If A is the area of a circle with radius r and...Ch. 3.9 - Each side of a square is increasing at a rate of 6...Ch. 3.9 - The radius of a sphere is increasing at a rate of...Ch. 3.9 - The radius of a spherical ball is increasing at a...Ch. 3.9 - The length of a rectangle is increasing at a rate...Ch. 3.9 - A cylindrical tank with radius 5m is being filled...Ch. 3.9 - The area of a triangle with sides of lengths a and...Ch. 3.9 - Prob. 9E Ch. 3.9 - If x2 + y2 + z2 = 9, dx/dt = 5, and dy/dt = 4,...Ch. 3.9 - The weight w of an astronaut (in pounds) is...Ch. 3.9 - A particle is moving along a hyperbola xy = 8. As...Ch. 3.9 - (a) What quantities are given in the problem? (b)...Ch. 3.9 - (a) What quantities are given in the problem? (b)...Ch. 3.9 - (a) What quantities are given in the problem? (b)...Ch. 3.9 - (a) What quantities are given in the problem? (b)...Ch. 3.9 - Two cars start moving from the same point. One...Ch. 3.9 - A spotlight on the ground shines on a wall 12m...Ch. 3.9 - A man starts walking north at 4 ft/s from a point...Ch. 3.9 - A baseball diamond is a square with side 90 ft. A...Ch. 3.9 - The altitude of a triangle is increasing at a rate...Ch. 3.9 - A boat is pulled into a dock by a rope attached to...Ch. 3.9 - Use the fact that the distance (in meters) a...Ch. 3.9 - Prob. 24E Ch. 3.9 - Water is leaking out of an inverted conical tank...Ch. 3.9 - Prob. 26E Ch. 3.9 - A water trough is 10m long and a cross-section has...Ch. 3.9 - A trough is 10 ft long and its ends have the shape...Ch. 3.9 - Gravel is being dumped from a conveyor belt at a...Ch. 3.9 - A swimming pool is 20 ft wide, 40 ft long, 3 ft...Ch. 3.9 - The sides of an equilateral triangle are...Ch. 3.9 - A kite 100ft above the ground moves horizontally...Ch. 3.9 - A car is traveling north on a straight road at...Ch. 3.9 - If the minute hand of a clock has length r (in...Ch. 3.9 - How fast is the angle between the ladder and the...Ch. 3.9 - According to the model we used to solve Example 2,...Ch. 3.9 - Boyles Law states that when a sample of gas is...Ch. 3.9 - A faucet is filling a hemispherical basin of...Ch. 3.9 - If two resistors with resistances R1 and R2 are...Ch. 3.9 - When air expands adiabatically (without gaining or...Ch. 3.9 - Prob. 41E Ch. 3.9 - Brain weight B as a function of body weight Win...Ch. 3.9 - Two sides of a triangle have lengths 12m and 15m ....Ch. 3.9 - Two carts, A and B, are connected by a rope 39 ft...Ch. 3.9 - A television camera is positioned 4000 ft from the...Ch. 3.9 - A lighthouse is located on a small island 3 km...Ch. 3.9 - A plane flies horizontally at an altitude of 5 km...Ch. 3.9 - A Ferris wheel with a radius of 10m is rotating at...Ch. 3.9 - A plane flying with a constant speed of 300 km/h...Ch. 3.9 - Two people start from the same point. One walks...Ch. 3.9 - A runner sprints around a circular track of radius...Ch. 3.9 - The minute hand on a watch is 8 mm long and the...Ch. 3.9 - Prob. 53E Ch. 3.10 - Find the linearization L(x) of the function at n....Ch. 3.10 - Find the linearization L(x) of the function at a ....Ch. 3.10 - Find the linearization L(x) of the function at a ....Ch. 3.10 - Prob. 4E Ch. 3.10 - Find the linear approximation of the function...Ch. 3.10 - Find the linear approximation of the function...Ch. 3.10 - Prob. 7E Ch. 3.10 - Prob. 8E Ch. 3.10 - Verify the given linear approximation at a = 0....Ch. 3.10 - Find the differential of the function. 11. y=e5x Ch. 3.10 - Find the differential of the function. 12. y=1t4 Ch. 3.10 - Find the differential of the function. 13....Ch. 3.10 - Prob. 14E Ch. 3.10 - Find the differential of the function. 15. y=1x23x Ch. 3.10 - Prob. 16E Ch. 3.10 - Find the differential of the function. 17....Ch. 3.10 - Prob. 18E Ch. 3.10 - (a) Find the differential dy and (b) evaluate dy...Ch. 3.10 - (a) Find the differential dy and (b) evaluate dy...Ch. 3.10 - (a) Find the differential dy and (b) evaluate dy...Ch. 3.10 - Prob. 22E Ch. 3.10 - Compute y and dy for the given values of x and dx...Ch. 3.10 - Compute y and dy for the given values of x and dx...Ch. 3.10 - Compute y and dy for the given values of x and dx...Ch. 3.10 - Prob. 26E Ch. 3.10 - Compare the values of y and dy if x changes from 1...Ch. 3.10 - Prob. 28E Ch. 3.10 - Prob. 29E Ch. 3.10 - Prob. 30E Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Explain, in terms of linear approximations or...Ch. 3.10 - Explain, in terms of linear approximations or...Ch. 3.10 - Prob. 40E Ch. 3.10 - The edge of a cube was found to be 30 cm with a...Ch. 3.10 - The radius of a circular disk is given as 24 cm...Ch. 3.10 - The circumference of a sphere was measured to be...Ch. 3.10 - Use differentials to estimate the amount of paint...Ch. 3.10 - (a) Use differentials to find a formula for the...Ch. 3.10 - One side of a right triangle is known to be 20 cm...Ch. 3.10 - If a current I passes through a resistor with...Ch. 3.10 - When blood flows along a blood vessel, the flux F...Ch. 3.10 - Establish the following rules for working with...Ch. 3.10 - Suppose that the only information we have about a...Ch. 3.10 - Suppose that we dont have a formula for g(x) but...Ch. 3.10 - Prob. 1DP Ch. 3.10 - Prob. 2DP Ch. 3.10 - Prob. 3DP Ch. 3.10 - Prob. 4DP Ch. 3.10 - Prob. 5DP Ch. 3.10 - Prob. 6DP Ch. 3.11 - Find the numerical value of each expression. 1....Ch. 3.11 - Find the numerical value of each expression. 2....Ch. 3.11 - Find the numerical value of each expression. 3....Ch. 3.11 - Find the numerical value of each expression. 4....Ch. 3.11 - Find the numerical value of each expression. 5....Ch. 3.11 - Prob. 6E Ch. 3.11 - Write 8sinhx+5coshx in terms of exandex .Ch. 3.11 - Write 2e2x+3e2x in terms of sinh2x and cosh2x .Ch. 3.11 - Write sinh(lnx) as a rational function of x .Ch. 3.11 - Prob. 10E Ch. 3.11 - Prove the identity. 7. sinh(x) = sinh x (This...Ch. 3.11 - Prob. 12E Ch. 3.11 - Prove the identity. 9. cosh x + sinh x = ex Ch. 3.11 - Prove the identity. 10. cosh x sinh r = ex Ch. 3.11 - Prove the identity. 11. sinh(x + y) = sinh x cosh...Ch. 3.11 - Prob. 16E Ch. 3.11 - Prove the identity. 13. coth2x 1 = csch2x Ch. 3.11 - Prove the identity. 14....Ch. 3.11 - Prove the identity. 15. sinh 2x = 2 sinh x cosh x Ch. 3.11 - Prob. 20E Ch. 3.11 - Prove the identity. 17. tanh(lnx)=x21x2+1 Ch. 3.11 - Prove the identity. 18. 1+tanhx1tanhx=e2x Ch. 3.11 - Prove the identity. 19. (cosh x + sinh x)n = cosh...Ch. 3.11 - If x=1213 find the values of the other hyperbolic...Ch. 3.11 - If cosh=53 and x 0. find the values of the other...Ch. 3.11 - Prob. 26E Ch. 3.11 - Use the definitions of the hyperbolic functions to...Ch. 3.11 - Prove the formulas given in Table 1 for the...Ch. 3.11 - Prob. 29E Ch. 3.11 - Prob. 30E Ch. 3.11 - Prob. 32E Ch. 3.11 - Prob. 33E Ch. 3.11 - Prob. 34E Ch. 3.11 - Prob. 35E Ch. 3.11 - Find the derivative. Simplify where possible. 30....Ch. 3.11 - Find the derivative. Simplify where possible. 33....Ch. 3.11 - Find the derivative. Simplify where possible. 32....Ch. 3.11 - Find the derivative. Simplify where possible. 35....Ch. 3.11 - Prob. 40E Ch. 3.11 - Find the derivative. Simplify where possible. 31....Ch. 3.11 - Prob. 42E Ch. 3.11 - Find the derivative. Simplify where possible. 39....Ch. 3.11 - Prob. 46E Ch. 3.11 - Prob. 47E Ch. 3.11 - Prob. 48E Ch. 3.11 - Prob. 49E Ch. 3.11 - Find the derivative. Simplify where possible. 51....Ch. 3.11 - Find the derivative. Simplify where possible. 42....Ch. 3.11 - Find the derivative. Simplify where possible. 43....Ch. 3.11 - Prob. 54E Ch. 3.11 - Prob. 55E Ch. 3.11 - The Gateway Arch The Gateway Arch in St. Louis was...Ch. 3.11 - Prob. 57E Ch. 3.11 - Prob. 58E Ch. 3.11 - Prob. 59E Ch. 3.11 - Prob. 60E Ch. 3.11 - Prob. 61E Ch. 3.11 - A model for the velocity of a falling object after...Ch. 3.11 - (a) Show that any function of the form y = A sinh...Ch. 3.11 - If x = ln( sec + tan ), show that sec = cosh x.Ch. 3.11 - At what point of the curve y = cosh x does the...Ch. 3.11 - Investigate the family of functions fn(x) = tanh...Ch. 3.11 - Prob. 67E Ch. 3 - State each differentiation rule both in symbols...Ch. 3 - State the derivative of each function. (a) y = xn...Ch. 3 - (a) How is the number e defined? (b) Express e as...Ch. 3 - (a) Explain how implicit differentiation works....Ch. 3 - Give several examples of how the derivative can be...Ch. 3 - Prob. 6CC Ch. 3 - (a) Write an expression for the linearization of f...Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Prob. 10TFQ Ch. 3 - Prob. 11TFQ Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Prob. 15TFQ Ch. 3 - Calculate y'. 1. y = (x2 + x3)4 Ch. 3 - Calculate y'. 2. y=1x1x35 Ch. 3 - Prob. 3E Ch. 3 - Calculate y'. 4. y=tanx1+cosx Ch. 3 - Prob. 5E Ch. 3 - Prob. 6E Ch. 3 - Prob. 7E Ch. 3 - Calculate y'. 8. xey = y sin x Ch. 3 - Calculate y'. 9. y = ln(x ln x)Ch. 3 - Prob. 10E Ch. 3 - Prob. 11E Ch. 3 - Calculate y'. 12. y = (arcsin 2x)2 Ch. 3 - Prob. 13E Ch. 3 - Calculate y'. 14. y = ln sec x Ch. 3 - Prob. 15E Ch. 3 - Prob. 16E Ch. 3 - Calculate y'. 17. y=arctan Ch. 3 - Prob. 18E Ch. 3 - Prob. 19E Ch. 3 - Prob. 20E Ch. 3 - Calculate y'. 21. y = 3x ln x Ch. 3 - Prob. 22E Ch. 3 - Prob. 23E Ch. 3 - Calculate y'. 24. y=1/x+x3 Ch. 3 - Prob. 25E Ch. 3 - Prob. 26E Ch. 3 - Prob. 27E Ch. 3 - Prob. 28E Ch. 3 - Calculate y'. 29. y=lnsinx12sin2x Ch. 3 - Prob. 30E Ch. 3 - Prob. 31E Ch. 3 - Prob. 32E Ch. 3 - Calculate y'. 33. y = ln | sec 5x + tan 5x |Ch. 3 - Prob. 34E Ch. 3 - Calculate y'. 35. y = cot(3x2 + 5)Ch. 3 - Prob. 36E Ch. 3 - Prob. 37E Ch. 3 - Calculate y . 38. y=xsec1x Ch. 3 - Prob. 39E Ch. 3 - Prob. 40E Ch. 3 - Prob. 42E Ch. 3 - Prob. 43E Ch. 3 - Prob. 45E Ch. 3 - Prob. 46E Ch. 3 - Prob. 47E Ch. 3 - Prob. 48E Ch. 3 - Calculate y'. 45. y = ln( cosh 3x)Ch. 3 - Prob. 50E Ch. 3 - Prob. 51E Ch. 3 - Prob. 52E Ch. 3 - Prob. 53E Ch. 3 - Prob. 54E Ch. 3 - Prob. 55E Ch. 3 - Prob. 56E Ch. 3 - Find y if x6 + y6 = 1.Ch. 3 - Find f(n)(x) if f(x) = 1/(2 x).Ch. 3 - Prob. 59E Ch. 3 - Prob. 60E Ch. 3 - Find an equation of the tangent to the curve at...Ch. 3 - Prob. 62E Ch. 3 - Prob. 63E Ch. 3 - Find equations of the tangent line and normal line...Ch. 3 - Find equations of the tangent line and normal line...Ch. 3 - If f(x) = xesin x find f(x). Graph f and f on the...Ch. 3 - Prob. 67E Ch. 3 - (a) If f(x) = 4x tan x, /2 x /2, find f and f....Ch. 3 - At what points on the curve y = sin x + cos x, 0 ...Ch. 3 - Prob. 70E Ch. 3 - Prob. 71E Ch. 3 - Prob. 72E Ch. 3 - Suppose that f(1) = 2 f(1) = 3 f(2) = 1 f'(2) = 2...Ch. 3 - If f and g are the functions whose graphs are...Ch. 3 - Find f in terms of g. f(x) = x2g(x)Ch. 3 - Prob. 76E Ch. 3 - Find f in terms of g. f(x) = [g(x)]2 Ch. 3 - Prob. 78E Ch. 3 - Find f in terms of g. f(x) = g(ex)Ch. 3 - Prob. 80E Ch. 3 - Prob. 81E Ch. 3 - Find f in terms of g. f(x) = g(ln x)Ch. 3 - Prob. 83E Ch. 3 - Prob. 84E Ch. 3 - Find f in terms of f and g. h(x) = f(g(sin 4x))Ch. 3 - Prob. 86E Ch. 3 - At what point on the curve y = [ln(x + 4)]2 is the...Ch. 3 - (a) Find an equation of the tangent to the curve y...Ch. 3 - Prob. 89E Ch. 3 - The function C(t) = K(eat ebt), where a, b, and K...Ch. 3 - Prob. 91E Ch. 3 - Prob. 92E Ch. 3 - A particle moves on a vertical line so that its...Ch. 3 - Prob. 94E Ch. 3 - Prob. 95E Ch. 3 - Prob. 96E Ch. 3 - A bacteria culture contains 200 cells initially...Ch. 3 - Cobalt-60 has a half-life of 5.24 years. (a) Find...Ch. 3 - Let C(t) be the concentration of a drug in the...Ch. 3 - A cup of hot chocolate has temperature 80C in a...Ch. 3 - Prob. 101E Ch. 3 - A paper cup has the shape of a cone with height 10...Ch. 3 - A balloon is rising at a constant speed of 5 ft/s....Ch. 3 - Prob. 104E Ch. 3 - Prob. 105E Ch. 3 - (a) Find the linear approximation to f(x)=25x2...Ch. 3 - (a) Find the linearization of f(x)1+3x3 at a = 0....Ch. 3 - Prob. 108E Ch. 3 - A window has the shape of a square surmounted by a...Ch. 3 - Prob. 110E Ch. 3 - Prob. 111E Ch. 3 - Express the limit as a derivative and evaluate....Ch. 3 - Prob. 113E Ch. 3 - Suppose f is a differentiable function such that...Ch. 3 - Prob. 115E Ch. 3 - Show that the length of the portion of any tangent...Ch. 3 - Find points P and Q on the parabola y = 1 x2 so...Ch. 3 - Prob. 2P Ch. 3 - Prob. 3P Ch. 3 - Prob. 4P Ch. 3 - If f(x)=limtxsectsecxtx, find the value of f'(/4).Ch. 3 - Find the values of the constants a and b such that...Ch. 3 - Show that sin-1(tanh x) = tan1(sinh x).Ch. 3 - Prob. 8P Ch. 3 - Prove that dndxn(sin4x+cos4x)=4n1cos(4x+n/2).Ch. 3 - Prob. 10P Ch. 3 - Prob. 11P Ch. 3 - Find all values of r such that the parabolas y =...Ch. 3 - How many lines are tangent to both of the circles...Ch. 3 - Prob. 14P Ch. 3 - The figure shows a rotating wheel with radius 40...Ch. 3 - Tangent lines T1, and T2, are drawn at two points...Ch. 3 - Prob. 17P Ch. 3 - Prob. 18P Ch. 3 - Prob. 19P Ch. 3 - Prob. 20P Ch. 3 - (a) Use the identity for tan(x y) (see Equation...Ch. 3 - Prob. 22P Ch. 3 - Prob. 23P Ch. 3 - Prob. 24P Ch. 3 - Prob. 25P Ch. 3 - Prob. 26P Ch. 3 - For what value of k does the equation e2x=kx have...Ch. 3 - Prob. 28P Ch. 3 - If y=xa212a21arctansinxa+a21+cosx show that...Ch. 3 - Given an ellipse x2/a2 + y2/b2 = 1, where a b,...Ch. 3 - Find the two points on the curve y = x4 2x2 x...Ch. 3 - Suppose that three points on the parabola y = x2...Ch. 3 - Prob. 33P Ch. 3 - Prob. 34P Ch. 3 - Prob. 35P

Knowledge Booster

Background pattern image

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning

Text book image

College Algebra

Algebra

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:Cengage Learning

SEE MORE TEXTBOOKS

Chain Rule dy:dx = dy:du*du:dx; Author: Robert Cappetta;https://www.youtube.com/watch?v=IUYniALwbHs;License: Standard YouTube License, CC-BY

CHAIN RULE Part 1; Author: Btech Maths Hub;https://www.youtube.com/watch?v=TIAw6AJ_5Po;License: Standard YouTube License, CC-BY