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Math Calculus Calculus Early Transcendentals, Binder Ready Version

Find the equation of the tangent line to the graph of y = f x at x = x 0 . f x = ln x ; x 0 = e − 1

Find the equation of the tangent line to the graph of y = f x at x = x 0 . f x = ln x ; x 0 = e − 1

Calculus Early Transcendentals, Binder Ready Version

Calculus Early Transcendentals, Binder Ready Version

11th Edition

ISBN: 9781118883822

Author: Howard Anton, Irl C. Bivens, Stephen Davis

Publisher: WILEY

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Concept explainers

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Textbook Question

Chapter 3.2, Problem 41ES

Find the equation of the tangent line to the graph of y = f x at x = x 0 .

f x = ln x ; x 0 = e − 1

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Chapter 3.2, Problem 40ES

Chapter 3.2, Problem 42ES

Chapter 3 Solutions

Calculus Early Transcendentals, Binder Ready Version

Ch. 3.1 - The equation xy+2y=1 defines implicitly the...Ch. 3.1 - Use implicit differentiation to find dy/dx for...Ch. 3.1 - The slope of the tangent line to the graph of...Ch. 3.1 - Use implicit differentiation to find d2y/dx2 for...Ch. 3.1 - (a) Find dy/dx by differentiating implicitly. (b)...Ch. 3.1 - (a) Find dy/dx by differentiating implicitly. (b)...Ch. 3.1 - Find dy/dx by implicit differentiation. x2+y2=100 Ch. 3.1 - Find dy/dx by implicit differentiation. x3+y3=3xy2 Ch. 3.1 - Find dy/dx by implicit differentiation....Ch. 3.1 - Find dy/dx by implicit differentiation....

Ch. 3.1 - Find dy/dx by implicit differentiation. 1x+1y=1 Ch. 3.1 - Find dy/dx by implicit differentiation. x2=x+yxy Ch. 3.1 - Find dy/dx by implicit differentiation. sinx2y2=x Ch. 3.1 - Find dy/dx by implicit differentiation. cosxy2=y Ch. 3.1 - Find dy/dx by implicit differentiation....Ch. 3.1 - Find dy/dx by implicit differentiation....Ch. 3.1 - Find d2y/dx2 by implicit differentiation. 2x23y2=4 Ch. 3.1 - Find d2y/dx2 by implicit differentiation. x3+y3=1 Ch. 3.1 - Find d2y/dx2 by implicit differentiation. x3y34=0 Ch. 3.1 - Find d2y/dx2 by implicit differentiation. xy+y2=2 Ch. 3.1 - Find d2y/dx2 by implicit differentiation. y+siny=x Ch. 3.1 - Find d2y/dx2 by implicit differentiation. xcosy=y Ch. 3.1 - Find the slope of the tangent line to the curve at...Ch. 3.1 - Find the slope of the tangent line to the curve at...Ch. 3.1 - True-False Determine whether the statement is true...Ch. 3.1 - True-False Determine whether the statement is true...Ch. 3.1 - True-False Determine whether the statement is true...Ch. 3.1 - True-False Determine whether the statement is true...Ch. 3.1 - Use implicit differentiation to find the slope of...Ch. 3.1 - Use implicit differentiation to find the slope of...Ch. 3.1 - Use implicit differentiation to find the slope of...Ch. 3.1 - Use implicit differentiation to find the slope of...Ch. 3.1 - Use implicit differentiation to find the specified...Ch. 3.1 - Use implicit differentiation to find the specified...Ch. 3.1 - Use implicit differentiation to find the specified...Ch. 3.1 - Use implicit differentiation to find the specified...Ch. 3.1 - As shown in the accompanying figure, it appears...Ch. 3.1 - (a) A student claims that the ellipse x2xy+y2=1...Ch. 3.1 - (a) Use the implicit plotting capability of a CAS...Ch. 3.1 - Use implicit differentiation to find all points on...Ch. 3.1 - Find the values of a and b for the curve x2y+ay2=b...Ch. 3.1 - At what point(s) is the tangent line to the curve...Ch. 3.1 - Two curves are said to be orthogonal if their...Ch. 3.1 - Two curves are said to be orthogonal if their...Ch. 3.1 - (a) Use the implicit plotting capability of a CAS...Ch. 3.1 - (a) Use the implicit plotting capability of a CAS...Ch. 3.1 - Find dy/dx if 2y3t+t3y=1 and dtdx=1cost Ch. 3.1 - Find equations for two lines through the origin...Ch. 3.1 - A student asks: â€œSuppose implicit...Ch. 3.2 - The equation of the tangent line to the graph of...Ch. 3.2 - Find dy/dx . (a) y=ln3x (b) y=lnx (c) y=log1/x Ch. 3.2 - Use logarithmic differentiation to find the...Ch. 3.2 - limh0ln1+hh=Ch. 3.2 - Find dy/dx . y=ln5x Ch. 3.2 - Find . Ch. 3.2 - Find dy/dx . y=ln1+x Ch. 3.2 - Find dy/dx . y=ln2+x Ch. 3.2 - Find dy/dx . y=lnx21 Ch. 3.2 - Find dy/dx . y=lnx37x23 Ch. 3.2 - Find . Ch. 3.2 - Find dy/dx . y=ln1+x1x Ch. 3.2 - Find . Ch. 3.2 - Find dy/dx . y=lnx3 Ch. 3.2 - Find dy/dx . y=lnx Ch. 3.2 - Find . Ch. 3.2 - Find dy/dx . y=xlnx Ch. 3.2 - Find . Ch. 3.2 - Find dy/dx . y=x2log232x Ch. 3.2 - Find dy/dx . y=xlog2x22x3 Ch. 3.2 - Find dy/dx . y=x21+logx Ch. 3.2 - Find dy/dx . y=logx1+logx Ch. 3.2 - Find dy/dx . y=lnlnx Ch. 3.2 - Find dy/dx . y=lnlnlnx Ch. 3.2 - Find dy/dx . y=lntanx Ch. 3.2 - Find dy/dx . y=lncosx Ch. 3.2 - Find dy/dx . y=coslnx Ch. 3.2 - Find dy/dx . y=sin2lnx Ch. 3.2 - Find dy/dx . y=logsin2x Ch. 3.2 - Find dy/dx . y=log1sin2x Ch. 3.2 - Use the method of Example 3 to help perform the...Ch. 3.2 - Use the method of Example 3 to help perform the...Ch. 3.2 - Use the method of Example 3 to help perform the...Ch. 3.2 - Use the method of Example 3 to help perform the...Ch. 3.2 - Determine whether the statement is true or false....Ch. 3.2 - Determine whether the statement is true or false....Ch. 3.2 - Determine whether the statement is true or false....Ch. 3.2 - Determine whether the statement is true or false....Ch. 3.2 - Find dy/dx using logarithmic differentiation....Ch. 3.2 - Find dy/dx using logarithmic differentiation....Ch. 3.2 - Find dy/dx using logarithmic differentiation....Ch. 3.2 - Find dy/dx using logarithmic differentiation....Ch. 3.2 - Find (a) ddxlogxe (b) ddxlogx2.Ch. 3.2 - Find (a) ddxlog1/xe (b) ddxloglnxe.Ch. 3.2 - Find the equation of the tangent line to the graph...Ch. 3.2 - Find the equation of the tangent line to the graph...Ch. 3.2 - Find the equation of the tangent line to the graph...Ch. 3.2 - Find the equation of the tangent line to the graph...Ch. 3.2 - (a) Find the equation of a line through the origin...Ch. 3.2 - Use logarithmic differentiation to verify the...Ch. 3.2 - Find a formula for the area Aw of the triangle...Ch. 3.2 - Find a formula for the area Aw of the triangle...Ch. 3.2 - Verify that y=lnx+e satisfies dy/dx=ey , with y=1...Ch. 3.2 - Verify that y=lne2x satisfies dy/dx=ey , with y=2...Ch. 3.2 - Find a function 0 such that y=fx satisfies...Ch. 3.2 - Find a function f such that y=fx satisfies...Ch. 3.2 - Find the limit by interpreting the expression as...Ch. 3.2 - Find the limit by interpreting the expression as...Ch. 3.2 - Find the limit by interpreting the expression as...Ch. 3.2 - Modify the derivation of Equation (2) to give...Ch. 3.2 - Let p denote the number of paramecia in a nutrient...Ch. 3.2 - One model for the spread of information over time...Ch. 3.2 - Show that the formula for dy/dx obtained in the...Ch. 3.3 - Suppose that a one-to-one function f has tangent...Ch. 3.3 - In each case, from the given derivative, determine...Ch. 3.3 - Evaluate the derivative. (a) (b) (c) (d) Ch. 3.3 - Let fx=ex3+x . Use fx to verify that f is...Ch. 3.3 - Let fx=x5+x3+x . (a) Show that f is one-to-one and...Ch. 3.3 - Let fx=x3+2ex . (a) Show that f is one-to-one and...Ch. 3.3 - Find f1x using Formula (2), and check your answer...Ch. 3.3 - Find f1x using Formula (2), and check your answer...Ch. 3.3 - Determine whether the function f is one-to-one by...Ch. 3.3 - Determine whether the function f is one-to-one by...Ch. 3.3 - Find the derivative of f1 by using Formula (3),...Ch. 3.3 - Find the derivative of f1 by using Formula (3),...Ch. 3.3 - Find the derivative of f1 by using Formula (3),...Ch. 3.3 - Find the derivative of f1 by using Formula (3),...Ch. 3.3 - Complete each part to establish that the...Ch. 3.3 - Prove that the reflection about the line y=x of a...Ch. 3.3 - Suppose that and are increasing functions....Ch. 3.3 - Suppose that f and g are one-to-one functions....Ch. 3.3 - Find dy/dx . y=e7x Ch. 3.3 - Find dy/dx . y=e5x2 Ch. 3.3 - Find dy/dx . y=x3ex Ch. 3.3 - Find dy/dx . y=e1/x Ch. 3.3 - Find dy/dx . y=exexex+ex Ch. 3.3 - Find dy/dx . y=sinex Ch. 3.3 - Find dy/dx . y=extanx Ch. 3.3 - Find dy/dx . y=exlnx Ch. 3.3 - Find dy/dx . y=exe3x Ch. 3.3 - Find dy/dx . y=exp1+5x3 Ch. 3.3 - Find dy/dx . y=ln1xex Ch. 3.3 - Find dy/dx . y=lncosex Ch. 3.3 - Find fx by Formula (7) and then by logarithmic...Ch. 3.3 - Find fx by Formula (7) and then by logarithmic...Ch. 3.3 - Find fx by Formula (7) and then by logarithmic...Ch. 3.3 - Find fx by Formula (7) and then by logarithmic...Ch. 3.3 - Find dy/dx using the method of logarithmic...Ch. 3.3 - Find dy/dx using the method of logarithmic...Ch. 3.3 - Find dy/dx using the method of logarithmic...Ch. 3.3 - Find dy/dx using the method of logarithmic...Ch. 3.3 - Find dy/dx using the method of logarithmic...Ch. 3.3 - (a) Explain why Formula (5) cannot be used to find...Ch. 3.3 - Find dy/dx using any method. y=x32x2+1ex Ch. 3.3 - Find dy/dx using any method. y=2x22x+1e2x Ch. 3.3 - Find dy/dx using any method. y=x2+x3x Ch. 3.3 - Find dy/dx using any method. y=x3+x35x Ch. 3.3 - Find dy/dx using any method. y=43sinxex Ch. 3.3 - Find dy/dx using any method. y=2cosx+lnx Ch. 3.3 - Find dy/dx . y=sin13x Ch. 3.3 - Find dy/dx . y=cos1x+12 Ch. 3.3 - Find dy/dx . y=sin11/x Ch. 3.3 - Find dy/dx . y=cos1cosx Ch. 3.3 - Find dy/dx . y=tan1x3 Ch. 3.3 - Find dy/dx . y=sec1x5 Ch. 3.3 - Find dy/dx . y=tanx1 Ch. 3.3 - Find dy/dx . y=1tan1x Ch. 3.3 - Find dy/dx . y=exsec1x Ch. 3.3 - Find dy/dx . y=lncos1x Ch. 3.3 - Find dy/dx . y=sin1x+cos1x Ch. 3.3 - Find dy/dx . y=x2sin1x3 Ch. 3.3 - Find dy/dx . y=sec1x+csc1x Ch. 3.3 - Find dy/dx . y=csc1ex Ch. 3.3 - Find dy/dx . y=cot1x Ch. 3.3 - Find dy/dx . y=cot1x Ch. 3.3 - Determine whether the statement is true or false....Ch. 3.3 - Determine whether the statement is true or false....Ch. 3.3 - Determine whether the statement is true or false....Ch. 3.3 - Determine whether the statement is true or false....Ch. 3.3 - (a) Use Formula (2) to prove that ddxcot1xx=0=1...Ch. 3.3 - (a) Use part (c) of Exercise 30 in Section 1.7 and...Ch. 3.3 - Find dy/dx by implicit differentiation....Ch. 3.3 - Find dy/dx by implicit differentiation....Ch. 3.3 - (a) Show that fx=x33x2+2x is not one-to-one on ,+...Ch. 3.3 - (a) Show that fx=x42x3 is not one-to-one on ,+ ....Ch. 3.3 - Let fx=x4+x3+1,0x2 . (a) Show that f is...Ch. 3.3 - Let fx=exp4x2x,x0 . (a) Show that f is one-to-one....Ch. 3.3 - Show that for any constant A and k , then function...Ch. 3.3 - Show that for any constants A and B , the function...Ch. 3.3 - Show that (a) y=xex satisfies the equation xy=1xy...Ch. 3.3 - Suppose that a new car is purchased for $20,000...Ch. 3.3 - Suppose that the percentage of U.S. households...Ch. 3.3 - Suppose that the population of oxygen-dependent...Ch. 3.3 - Find the limit by interpreting the expression as...Ch. 3.3 - Find the limit by interpreting the expression as...Ch. 3.3 - Find the limit by interpreting the expression as...Ch. 3.3 - Find the limit by interpreting the expression as...Ch. 3.3 - Find the limit by interpreting the expression as...Ch. 3.3 - Find the limit by interpreting the expression as...Ch. 3.3 - Suppose that a steel ball bearing is released...Ch. 3.4 - If A=x2 and dxdt=3 , find dAdtx=10.Ch. 3.4 - If A=x2 and dAdt=3 , find dxdtx=10.Ch. 3.4 - A 10-foot ladder stands on a horizontal floor and...Ch. 3.4 - Suppose that a block of ice in the shape of a...Ch. 3.4 - Both x and y denote functions of t that are...Ch. 3.4 - Both x and y denote functions of t that are...Ch. 3.4 - Both x and y denote functions of t that are...Ch. 3.4 - Both x and y denote functions of t that are...Ch. 3.4 - Let A be the area of a square whose sides have...Ch. 3.4 - Prob. 6ES Ch. 3.4 - Let V be the volume of a cylinder having height h...Ch. 3.4 - Let l be the length of a diagonal of a rectangle...Ch. 3.4 - Let (in radians) be an acute angle in a right...Ch. 3.4 - Suppose that z=x3y2 , where both x and y are...Ch. 3.4 - The minute hand of a certain clock is 4in long....Ch. 3.4 - A stone dropped into a still pond sends out a...Ch. 3.4 - Oil spilled from a ruptured tanker spreads in a...Ch. 3.4 - A spherical balloon is inflated so that its volume...Ch. 3.4 - A spherical balloon is to be deflated so that its...Ch. 3.4 - A 17ft ladder is leaning against a wall. If the...Ch. 3.4 - A 13ft ladder is leaning against a wall. If the...Ch. 3.4 - A 10ft plank is leaning against a wall. If at a...Ch. 3.4 - A softball diamond is a square whose sides are...Ch. 3.4 - A rocket, rising vertically, is tracked by a radar...Ch. 3.4 - For the camera and rocket shown in Figure 3.4.5,...Ch. 3.4 - For the camera and rocket shown in Figure 3.4.5,...Ch. 3.4 - A satellite is in an elliptical orbit around the...Ch. 3.4 - An aircraft is flying horizontally at a constant...Ch. 3.4 - A conical water tank with vertex down has a radius...Ch. 3.4 - Grain pouring from a chute at the rate of 8ft3/min...Ch. 3.4 - Sand pouring from a chute forms a conical pile...Ch. 3.4 - Wheat is poured through a chute at the rate of...Ch. 3.4 - An aircraft is climbing at a 30 angle to the...Ch. 3.4 - A boat is pulled into a dock by means of a rope...Ch. 3.4 - For the boat in Exercise 30, how fast must the...Ch. 3.4 - A man 6ft tall is walking at the rate of 3ft/s...Ch. 3.4 - A beacon that makes one revolution every 10s is...Ch. 3.4 - An aircraft is flying at a constant altitude with...Ch. 3.4 - Solve Exercise 34 under the assumption that the...Ch. 3.4 - A police helicopter is flying due north at 100mi/h...Ch. 3.4 - Prob. 37ES Ch. 3.4 - A point P is moving along the curve whose equation...Ch. 3.4 - A point P is moving along the line whose equation...Ch. 3.4 - Prob. 40ES Ch. 3.4 - A particle is moving along the curve y=x/x2+1 ....Ch. 3.4 - A new design for a wind turbine adjusts the length...Ch. 3.4 - The thin lens equation in physics is 1s+1S=1f...Ch. 3.4 - Water is stored in a cone-shaped reservoir (vertex...Ch. 3.4 - A meteor enters the Earthâ€™s atmosphere and bums...Ch. 3.4 - On a certain clock the minute hand is 4in long and...Ch. 3.4 - Coffee is poured at a uniform rate of 20cm3/s into...Ch. 3.5 - The local linear approximation of f at x0 use the ...Ch. 3.5 - Find an equation for the local linear...Ch. 3.5 - Let y=5x2 . Find dy and y at x=2 with dx=x=0.1 .Ch. 3.5 - Prob. 4QCE Ch. 3.5 - (a) Use Formula (1) to obtain the local linear...Ch. 3.5 - (a) Use Formula (1) to obtain the local linear...Ch. 3.5 - (a) Find the local linear approximation of the...Ch. 3.5 - A student claims that whenever a local linear...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the stated formula is the local...Ch. 3.5 - Confirm that the formula is the local linear...Ch. 3.5 - Confirm that the formula is the local linear...Ch. 3.5 - Confirm that the formula is the local linear...Ch. 3.5 - Confirm that the formula is the local linear...Ch. 3.5 - (a) Use the local linear approximation of sinx at...Ch. 3.5 - (a) Use the local linear approximation of at to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - Use an appropriate local linear approximation to...Ch. 3.5 - The approximation 1+xk1+kx is commonly used by...Ch. 3.5 - Use the approximation 1+xk1+kx , along with some...Ch. 3.5 - Referring to the accompanying figure, suppose that...Ch. 3.5 - Prob. 37ES Ch. 3.5 - (a) Let y=x . Find dy and y at x=9 with dx=x=1 ....Ch. 3.5 - Find formulas for and . Ch. 3.5 - Find formulas for and . Ch. 3.5 - Find formulas for dy and y . y=x22x+1 Ch. 3.5 - Find formulas for and . Ch. 3.5 - Find the differential dy . (a) y=4x37x2 (b)...Ch. 3.5 - Find the differential . (a) (b) Ch. 3.5 - Find the differential dy . (a) y=x1x (b) y=1+x17 Ch. 3.5 - Find the differential dy . (a) y=1x31 (b) y=1x32x Ch. 3.5 - Determine whether the statement is true or false....Ch. 3.5 - Determine whether the statement is true or false....Ch. 3.5 - Determine whether the statement is true or false....Ch. 3.5 - Determine whether the statement is true or false....Ch. 3.5 - Use the differential to approximate when ...Ch. 3.5 - Use the differential dy to approximate y when x...Ch. 3.5 - Use the differential dy to approximate y when x...Ch. 3.5 - Use the differential dy to approximate y when x...Ch. 3.5 - The side of a square is measured to be 10ft , with...Ch. 3.5 - The side of a cube is measured to be 25cm , with a...Ch. 3.5 - The hypotenuse of a right triangle is known to be...Ch. 3.5 - One side of a right triangle is known to be 25cm...Ch. 3.5 - The electrical resistance R of a certain wire is...Ch. 3.5 - A long high-voltage power line is 18feet above the...Ch. 3.5 - The area of a right triangle with a hypotenuse of...Ch. 3.5 - The side of a square is measured with a possible...Ch. 3.5 - The side of a cube is measured with a possible...Ch. 3.5 - The volume of a sphere is to be computed from a...Ch. 3.5 - The area of a circle is to be computed from a...Ch. 3.5 - A steel cube with 1-inch sides is coated with...Ch. 3.5 - A metal rod 15cm long and 5cm in diameter is to be...Ch. 3.5 - The time required for one complete oscillation of...Ch. 3.5 - The magnitude R of an earthquake on the Richter...Ch. 3.5 - Suppose that the time T (in days) for a cancerous...Ch. 3.5 - Explain why the local linear approximation of a...Ch. 3.6 - Prob. 1QCE Ch. 3.6 - Evaluate each of the limits in Quick Check...Ch. 3.6 - Using Lâ€™Hopitalâ€™s rule, limx+ex500x2=.Ch. 3.6 - Evaluate the given limit without using...Ch. 3.6 - Evaluate the given limit without using...Ch. 3.6 - Determine whether the statement is true or false....Ch. 3.6 - Determine whether the statement is true or false....Ch. 3.6 - Determine whether the statement is true or false....Ch. 3.6 - Determine whether the statement is true or false....Ch. 3.6 - Find the limits. limx0ex1sinx Ch. 3.6 - Find the limits. limx0sin2xsin5x Ch. 3.6 - Prob. 9ES Ch. 3.6 - Find the limits. limt0tet1et Ch. 3.6 - Prob. 11ES Ch. 3.6 - Prob. 12ES Ch. 3.6 - Find the limits. limx+lnxx Ch. 3.6 - Find the limits. limx+e3xx2 Ch. 3.6 - Find the limits. limx0+cotxlnx Ch. 3.6 - Find the limits. limx0+1lnxe1/x Ch. 3.6 - Find the limits. limx+x100ex Ch. 3.6 - Find the limits. limx0+lnsinxlntanx Ch. 3.6 - Find the limits. limx0sin12xx Ch. 3.6 - Find the limits. limx0xtan1xx3 Ch. 3.6 - Find the limits. limx+xex Ch. 3.6 - Find the limits. limxxtan12x Ch. 3.6 - Find the limits. limx+xsinx Ch. 3.6 - Find the limits. limx0+tanxlnx Ch. 3.6 - Prob. 25ES Ch. 3.6 - Find the limits. limxxcotx Ch. 3.6 - Find the limits. limx+13/xx Ch. 3.6 - Find the limits. limx01+2x3/x Ch. 3.6 - Prob. 29ES Ch. 3.6 - Find the limits. limx+1+a/xbx Ch. 3.6 - Prob. 31ES Ch. 3.6 - Find the limits. limx+cos2/xx2 Ch. 3.6 - Find the limits. limx0cscx1/x Ch. 3.6 - Find the limits. limx01x2cos3xx2 Ch. 3.6 - Find the limits. limx+x2+xx Ch. 3.6 - Find the limits. limx01x1ex1 Ch. 3.6 - Find the limits. limx+xlnx2+1 Ch. 3.6 - Find the limits. limx+lnxln1+x Ch. 3.6 - Find the limits. limx0+xsinx Ch. 3.6 - Find the limits. limx0+e2x1x Ch. 3.6 - Find the limits. limx0+1lnxx Ch. 3.6 - Find the limits. limx+x1/x Ch. 3.6 - Find the limits. limx+lnx1/x Ch. 3.6 - Find the limits. limx0+lnxx Ch. 3.6 - Prob. 45ES Ch. 3.6 - Show that for any positive integer n (a)...Ch. 3.6 - (a) Find the error in the following calculation:...Ch. 3.6 - (a) Find the error in the following calculation:...Ch. 3.6 - Make a conjecture about the limit by graphing the...Ch. 3.6 - Make a conjecture about the limit by graphing the...Ch. 3.6 - Make a conjecture about the limit by graphing the...Ch. 3.6 - Make a conjecture about the limit by graphing the...Ch. 3.6 - Make a conjecture about the equations of...Ch. 3.6 - Make a conjecture about the equations of...Ch. 3.6 - Make a conjecture about the equations of...Ch. 3.6 - Make a conjecture about the equations of...Ch. 3.6 - Prob. 57ES Ch. 3.6 - There is a myth that circulates among beginning...Ch. 3.6 - Verify that Lâ€™Hopitalâ€™s rule is of no help in...Ch. 3.6 - Verify that Lâ€™Hopitalâ€™s rule is of no help in...Ch. 3.6 - Verify that Lâ€™Hopitalâ€™s rule is of no help in...Ch. 3.6 - Verify that Lâ€™Hopitalâ€™s rule is of no help in...Ch. 3.6 - The accompanying schematic diagram represents an...Ch. 3.6 - (a) Show that limx/2/2xtanx=1 . (b) Show that...Ch. 3.6 - (a) Use a CAS to show that if k is a positive...Ch. 3.6 - Find all values of k and l such that...Ch. 3.6 - Let fx=x2sin1/x . (a) Are the limits limx0+fx and...Ch. 3.6 - (a) Explain why Lâ€™Hopitalâ€™s rule does not...Ch. 3.6 - Find limx0+xsin1/xsinx if it exists.Ch. 3.6 - Suppose that functions f and g are differentiable...Ch. 3.6 - Were we to use Lâ€™Hopitalâ€™s mle to evaluate...Ch. 3 - (a) Find dy/dx by differentiating implicitly, (b)...Ch. 3 - (a) Find dy/dx by differentiating implicitly, (b)...Ch. 3 - Find dy/dx by implicit differentiation. 1y+1x=1 Ch. 3 - Find dy/dx by implicit differentiation. x3y3=6xy Ch. 3 - Find dy/dx by implicit differentiation. secxy=y Ch. 3 - Find dy/dx by implicit differentiation....Ch. 3 - Find d2y/dx2 by implicit differentiation. 3x24y2=7 Ch. 3 - Find d2y/dx2 by implicit differentiation. 2xyy2=3 Ch. 3 - Use implicit differentiation to find the slope of...Ch. 3 - At what point(s) is the tangent line to the curve...Ch. 3 - Prove that if P and Q are two distinct points on...Ch. 3 - Find the coordinates of the point in the first...Ch. 3 - Find the coordinates of the point in the first...Ch. 3 - Use implicit differentiation to show that the...Ch. 3 - Find dy/dx by first using algebraic properties of...Ch. 3 - Find dy/dx by first using algebraic properties of...Ch. 3 - Find dy/dx . y=ln2x Ch. 3 - Find dy/dx . y=lnx2 Ch. 3 - Find dy/dx . y=lnx+13 Ch. 3 - Find dy/dx . y=lnx+13 Ch. 3 - Find dy/dx . y=loglnx Ch. 3 - Find dy/dx . y=1+logx1logx Ch. 3 - Find dy/dx . y=lnx3/21+x4 Ch. 3 - Find dy/dx . y=lnxcosx1+x2 Ch. 3 - Find dy/dx . y=elnx2+1 Ch. 3 - Find dy/dx . y=ln1+ex+e2x1e3x Ch. 3 - Find dy/dx . y=2xex Ch. 3 - Find dy/dx . y=a1+bex Ch. 3 - Find dy/dx . y=1tan12x Ch. 3 - Find dy/dx . y=2sin1x Ch. 3 - Find dy/dx . y=xex Ch. 3 - Find dy/dx . y=1+x1/x Ch. 3 - Find dy/dx . y=sec12x+1 Ch. 3 - Find dy/dx . y=cos1x2 Ch. 3 - Find dy/dx using logarithmic differentiation....Ch. 3 - Find dy/dx using logarithmic differentiation....Ch. 3 - (a) Make a conjecture about the shape of the graph...Ch. 3 - Recall from Section 1.8 that the loudness of a...Ch. 3 - A particle is moving along the curve y=xlnx . Find...Ch. 3 - Find the equation of the tangent fine to the graph...Ch. 3 - Find the value of b so that the line y=x is...Ch. 3 - In each part, find the value of k for which the...Ch. 3 - If f and g are inverse functions and f is...Ch. 3 - In each part, find f1x using Formula (2) of...Ch. 3 - Find a point on the graph of y=e3x at which the...Ch. 3 - Show that the rate of change of y=5000e1.07x is...Ch. 3 - Show that the rate of change of y=32x57x is...Ch. 3 - The equilibrium constant k of a balanced chemical...Ch. 3 - Show that the function y=eaxsinbx satisfies...Ch. 3 - Show that the function y=tan1x satisfies...Ch. 3 - Suppose that the population of deer on an island...Ch. 3 - In each part, find each limit by interpreting the...Ch. 3 - Suppose that limfx= and limgx= . In each of the...Ch. 3 - (a) Under what conditions will a limit of the form...Ch. 3 - Evaluate the given limit. limx+exx2 Ch. 3 - Evaluate the given limit. limx1lnxx41 Ch. 3 - Evaluate the given limit. limx0x2e2sin23x Ch. 3 - Evaluate the given limit. limx0ax1x,a0 Ch. 3 - An oil slick on a lake is surrounded by a floating...Ch. 3 - The hypotenuse of a right triangle is growing at a...Ch. 3 - In each part, use the given information to find...Ch. 3 - Use an appropriate local linear approximation to...Ch. 3 - The base of the Great Pyramid at Giza is a square...

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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY