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Math
Calculus
CALCULUS, EARLY TRANS. -WEBASSIGN ACCES
Chapter 3.4, Problem 100E
Chapter 3.4, Problem 100E
BUY
CALCULUS, EARLY TRANS. -WEBASSIGN ACCES
9th Edition
ISBN:
2819260099505
Author: Stewart
Publisher:
CENGAGE C
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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3.1 Derivatives Of Polynomials And Exponential Functions
3.2 The Product And Quotient Rules
3.3 Derivatives Of Trigonometric Functions
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives Of Logarithmic And Inverse Trigonometric Functions
3.7 Rates Of Change In The Natural And Social Sciences
3.8 Exponential Growth And Decay
3.9 Related Rates
3.10 Linear Approximations And Differentials
3.11 Hyperbolic Functions
Chapter Questions
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Problem 1E: Write the composite function in the form f(g(x)) . [Identify the inner function u=g(x) and the outer...
Problem 2E
Problem 3E: Write the composite function in the form f(g(x)) . [Identify the inner function u=g(x) and the outer...
Problem 4E: Write the composite function in the form f(g(x)) . [Identify the inner function u=g(x) and the outer...
Problem 5E: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the...
Problem 6E: Write the composite function in the form f(g(x)) . [Identify the inner function u=g(x) and the outer...
Problem 7E: Find the derivative of the function. 7. f(x)=2x35x2+45
Problem 8E: Find the derivative of the function. 8. f(x)=x5+3x2x50
Problem 9E: Find the derivative of the function. f(x)=5x+1
Problem 10E: Find the derivative of the function. f(x)=1x213
Problem 11E: Find the derivative of the function. 11. g(t)=1(2t+1)2
Problem 12E
Problem 13E: Find the derivative of the function. f() = cos(2)
Problem 14E: Find the derivative of the function. g() = cos2
Problem 15E: Find the derivative of the function. 15. g(x)=ex2x
Problem 16E: Find the derivative of the function. 16. y=5x
Problem 17E: Find the derivative of the function. y = x2e3x
Problem 18E: Find the derivative of the function. f(t) = t sin t
Problem 19E: Find the derivative of the function. f(t) = eat sin bt
Problem 20E
Problem 21E: Find the derivative of the function. 21. F(x)=(4x+5)3x22x+54
Problem 22E: Find the derivative of the function. 22. G(z)=(14z)2z2+1
Problem 23E: Find the derivative of the function. y=xx+1
Problem 24E: Find the derivative of the function. y=(x+1x)5
Problem 25E: Find the derivative of the function. y = e tan
Problem 26E: Find the derivative of the function. f(t)2t3
Problem 27E: Find the derivative of the function. g(u)=(u31u3+1)8
Problem 28E: Find the derivative of the function. s(t)=1+sint1+cost
Problem 29E: Find the derivative of the function. r(t)=10t2
Problem 30E: Find the derivative of the function. f(z) = ez/(z1)
Problem 31E: Find the derivative of the function. H(r)=(r21)3(2r+1)5
Problem 32E: Find the derivative of the function. J() = tan2(n)
Problem 33E: Find the derivative of the function. F(t) = et sin 2t
Problem 34E: Find the derivative of the function. F(t)=t2t3+1
Problem 35E: Find the derivative of the function. G(x) = 4C/x
Problem 36E
Problem 37E
Problem 38E
Problem 39E: Find the derivative of the function. 39. F(t)=tan1+t2
Problem 40E
Problem 41E: Find the derivative of the function. 41. y= sin 2 x 2 +1
Problem 42E: Find the derivative of the function. y = esin 2x + sin(e2x)
Problem 43E: Find the derivative of the function. 43. g(x)=sinex1+ex
Problem 44E: Find the derivative of the function. 44. f(t)=e1/tt21
Problem 45E: Find the derivative of the function. f(t) = tan(sec(cos t))
Problem 46E: Find the derivative of the function. y=x+x+x
Problem 47E: Find the derivative of the function. 47. f(x)=esin2x2
Problem 48E: Find the derivative of the function. y=234x
Problem 49E: Find the derivative of the function. 49. y=3cosx214
Problem 50E: Find the derivative of the function. 50. y=sin(+tan(+cos))
Problem 51E: Find the derivative of the function. y=cossin(tanx)
Problem 52E: Find the derivative of the function. 52. y=sin3cosx2
Problem 53E: Find y and y. y = cos(sin 3)
Problem 54E: Find y and y . 54. y=(1+x)3
Problem 55E
Problem 56E: Find y and y. y=eex
Problem 57E: Find an equation of the tangent line to the curve at the given point. y = 2x, (0. 1)
Problem 58E: Find an equation of the tangent line to the curve at the given point. y=1+x3,(2,3)
Problem 59E: Find an equation of the tangent line to the curve at the given point. y = sin(sin x), (, 0)
Problem 60E: Find an equation of the tangent line to the curve at the given point. y=xex2,(0,0)
Problem 61E
Problem 62E: (a) The curve y=|x|/2x2 is called a bullet-nose curve. Find an equation of the tangent line to this...
Problem 63E: (a) If f(x)=2x2x, find f(x). (b) Check to see that your answer to part (a) is reasonable by...
Problem 64E
Problem 65E: Find all points on the graph of the function f(x) = 2 sin x + sin2x at which the tangent line is...
Problem 66E: At what point on the curve y=1+2x is the tangent line perpendicular to the line 6x + 2y = 1?
Problem 67E: If F(x) = f(g(x)), where f(2) = 8, f(2) = 4, f(5) = 3, g(5) = 2, and g(5) = 6, find F(5).
Problem 68E: If h(x)=4+3f(x), where f(1) = 7andf(1) = 4, find h(1).
Problem 69E: A table of values for f, g, f, and g is given. (a) If h(x) = f(g(x)), find h(1). (b) If H(x) =...
Problem 70E: Let f and g be the functions in Exercise 69. (a) If F(x)=f(f(x)) , find F(2) . (b) If G(x)=g(g(x)) ,...
Problem 71E: If f and g are the functions whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) =...
Problem 72E: If f is the function whose graph is shown, let h(x) = f(f(x)) and g(x) = f(x2). Use the graph of f...
Problem 73E: If g(x)=f(x), where the graph off is shown, evaluate g(3).
Problem 74E
Problem 75E: Suppose f is differentiable on . Let F(x) = f(ex) and G(x) = ef(x). Find expressions for (a) F(x)...
Problem 76E: Let g(x) = ecx + f(x) and h(x) = ekxf(x), where f(0) = 3, f(0) = 5, and f(0) = 2. (a) Find g(0) and...
Problem 77E: Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h(1) = 4, g(2) = 5, and f(3) = 6. Find r(1).
Problem 78E: If g is a twice differentiable function and f(x) = xg(x2), find f in terms of g, g, and g.
Problem 79E
Problem 80E
Problem 81E: Show that the function y = e2x (A cos 3x + B sin 3x) satisfies the differential equation y 4y + 13y...
Problem 82E: For what values of r does the function y = erx satisfy the differential equation y 4y + y = 0?
Problem 83E: Find the 50th derivative of y = cos 2x.
Problem 84E
Problem 85E: The displacement of a particle on a vibrating string is given by the equation s(t)=10+14sin(10t)...
Problem 86E: If the equation of motion of a particle is given by s = A cos(t + ), the particle is said to undergo...
Problem 87E: A Cepheid variable star is a star whose brightness alternately increases and decreases. The most...
Problem 88E: In Example 1.3.4 we arrived at a model for the length of daylight (in hours) in Philadelphia on the...
Problem 89E
Problem 90E: Under certain circumstance a rumor spreads according to the equation p(t)=11+aekt where p(t) is the...
Problem 91E: The average blood alcohol concentration (BAC) of eight male subjects was measured after consumption...
Problem 92E: Air is being pumped into a spherical weather balloon. At any time t, the volume of the balloon is...
Problem 93E
Problem 94E
Problem 95E: Use the Chain Rule to prove the following. (a) The derivative of an even function is an odd...
Problem 96E
Problem 97E: Use the Chain Rule to show that if is measured in degrees, then dd(sin)=180cos (This gives one...
Problem 98E
Problem 99E
Problem 100E
Problem 101E
Problem 102E
Problem 1AP: An approach path for an aircraft landing is shown in the figure and satisfies the following...
Problem 2AP
Problem 3AP
Problem 4AP
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