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Calculus Single Variable Canadian 9th Edition Adams Test BankFull Download: lus, 9eChapter 2: DifferentiationChapter 2 Differentiation2.1 Tangent Lines and Their Slopes1) Find the slope of the tangent line to the curve y 4x A) -1B) 2C) 6D)at the point (-1, 0).E) -2Answer: CDiff: 12) Find the equation of the tangent line to the curve y 2x A) 2x y - 4 0B) 2x y 4 0C) 2x - y - 4 0D) 2x - y 4 0E) 2x y 0Answer: ADiff: 1at the point (2, 0).3) Find an equation of the line tangent to the curve y 2x -at the point where x 2.A) 25y 49x - 1B) 5y 49x 1C) 25y 49x 1D) 25y 41x 1E) 25x 49y 1Answer: CDiff: 24) Find an equation of the line tangent to the curve y A) y 12x 15B) y 12x -15C) y -12x -15D) y -12x 15E) y 15x 12Answer: BDiff: 2 1 at the point where x 2.Copyright 2018 Pearson Canada Inc.Full download all chapters instantly please go to Solutions Manual, Test Bank site: testbanklive.com2-1

Calculus, 9eChapter 2: Differentiation5) Find an equation of the line tangent to the curve y A) y -4x 12B) y 4x - 4C) y -4x 4D) y 4x 4E) y 4x - 12Answer: CDiff: 2at the point where x 2.6) Find an equation of the line tangent to the curve y at the point where x 11.A) y x B) y x C) y 4x D) y 4x E) y - x Answer: BDiff: 27) Find an equation of the line tangent to the curve y at the point (1, 3).A) y - x B) y - x C) y x D) y x-E) y 3x - 10Answer: ADiff: 2Copyright 2018 Pearson Canada Inc.2-2

Calculus, 9eChapter 2: Differentiation8) Let f(x) be a function such that - 1. Find the slope of the line tangent tothe graph of f at the point (a, f(a)).A) 3B) 1 C) -3D) - 1E)-a CAnswer: BDiff: 19) Find the point(s) on the curve y pass through (2, -12).A) (6, 36) and (-2, 4)B) (6, 36) and (2, 4)C) (-6, 36) and (-2, 4)D) (-6, 6) and (-2, 4)E) (6, -36) and (-2, 4)Answer: ADiff: 2such that the tangent lines to the curve at those points10) Find the standard equation of the circle with centre at (1, 3) which is tangent to the line 5x 12y 8.A) 1B) 9C) 9D) 8E) 8Answer: CDiff: 2Copyright 2018 Pearson Canada Inc.2-3

Calculus, 9eChapter 2: Differentiation11) If the line 4x - 9y 0 is tangent in the first quadrant to the graph of y c, what is thevalue of c?A) B)C)D)E)Answer: BDiff: 32.2 The Derivative1) Using the definition of the derivative, find the derivative of f(x) .A)B)C)D)E)Answer: DDiff: 1Copyright 2018 Pearson Canada Inc.2-4

Calculus, 9eChapter 2: Differentiation2) Find the derivative (x) of the function f(x) .A) B)C) D) E)Answer: ADiff: 23) Find the tangent line to the curve y at the origin.A) y - xB) y xC) y xD) y - xE) y xAnswer: CDiff: 24) Where is the function f(x) differentiable?A) at every x (- , )B) at every x (- , 0) (0, )C) at every x (- , 3) (3, )D) at every x (- , 0) (0, 3) (3, )E) none of the aboveAnswer: CDiff: 2Copyright 2018 Pearson Canada Inc.2-5

Calculus, 9eChapter 2: Differentiation5) Find the equation of the straight line that passes through the point P(0,- 3) and is tangent to thecurve.A) y -3B) y 2x - 3C) y -3xD) y -x - 3E) y x - 3Answer: BDiff: 36) If f(x) (), calculate f'(5) by using the definition of the derivative.A)B) C) D) E)Answer: BDiff: 27) Find the slope of the line tangent to the curvey 1 at the point.A)B) C) D)E)Answer: CDiff: 2Copyright 2018 Pearson Canada Inc.2-6

Calculus, 9eChapter 2: Differentiation8) If f(x) , calculate f'(-2) directly from the definition of the derivative.A) 3B) 3C) -3D) 4E) 2Answer: DDiff: 29) Let g(x) be a function such that -. Find(x).A)B) C) D)E)Answer: BDiff: 110) Calculate the derivative of g(t) A) 101- 99B) 101- 99C) -101- 99D) 100- 98E) 101 99Answer: ADiff: 2 using the general power rule.11) If f(x) is an even, differentiable function, thenA) is an odd function.B) is an even function.C) is neither odd nor even.D) may be either even or odd or neither.Answer: ADiff: 3(x)Copyright 2018 Pearson Canada Inc.2-7

Calculus, 9eChapter 2: Differentiation12) True or False: If the curve y f(x) has a tangent line at (a, f(a)), then f is differentiable atx a.Answer: FALSEDiff: 3 - , then the graph of f has a tangent line at x a.13) True or False: IfAnswer: TRUEDiff: 314) True or False: If f is continuous at x a, then f is differentiable at x a.Answer: FALSEDiff: 315) True or False: Ifexists, then f is continuous at x a.Answer: TRUEDiff: 316) True or False: The domain of the derivative of a function is the same as the domain of thefunction.Answer: FALSEDiff: 32.3 Differentiation Rules1) Differentiate f(x) 10 .A) 10B) 50C) 55D) 50E) 50xAnswer: BDiff: 12) Findif y 4 3 x - 6.A) 16 - 9 1B) 16 9 1C) 16 9 1D) 16 9 - 6E) 16 9 - 5Answer: CDiff: 1Copyright 2018 Pearson Canada Inc.2-8

Calculus, 9eChapter 2: Differentiation3) Differentiate the function f(x) (2A) 30 - 8 30x - 5B) 30 - 8 30x 5C) 30 8 30x - 5D) 30 8 - 30x - 5E) 36 - 6Answer: ADiff: 2 5)(3- x).4) Find the equation of the tangent line to the curve y (2 A) x - y 4 0B) x y - 6 0C) x - y - 4 0D) 6x - y - 1 0E) x y 4 0Answer: ADiff: 25) Find the points on the curve y A) ( , -5) and (- , -5)B) (0, 4), ( , -5), and (- , -5)C) (0, 4), (- , 5), and ( , -5)D) (0, 4), ( , -5), and (- , -5)E) ( , 5) and (- , 5)Answer: DDiff: 2-6)(1 3x) at the point (1, 5). 4 where the tangent line is horizontal.6) Given g(x) which of the following statements is true?A) g is differentiable at x -1B) g is not differentiable at x -1C) (-1) -4D) g is continuous at x -1E) g is continuous from the left at x -1Answer: BDiff: 3Copyright 2018 Pearson Canada Inc.2-9

Calculus, 9eChapter 2: Differentiation7) Lines passing through the point (0, 2) are tangent to the graph of y tangency.A) (1, -1) and (-1, 1)B) (2, -8) and (-2, -8)C) (1, -1) and (-2, -8)D) (2, -8) and (-1, 1)E) (1, 1) and (-1, -1)Answer: ADiff: 38) Where does the normal line to the curve y x second time?A) (-2, -6)B) (- , - ). Find the points ofat the point (1, 0) intersect the curve aC) (-1, -2)D) (0, 0)E) It does not intersect the curve a second time.Answer: CDiff: 39) Which of the following statements is always true?A) If f is continuous at c, then it must be differentiable at c.B) If f is differentiable at c, then it must be continuous at c.C) If f is not differentiable at c, then it must be discontinuous at c.D) Iff(c h) f(c), then f must be differentiable at c.E) All of the aboveAnswer: BDiff: 210) How many tangent lines to the graph of y A) 0B) 1C) 2D) 3E) 4Answer: EDiff: 3-15- 10 pass through the point (0, 2)?Copyright 2018 Pearson Canada Inc.2-10

Calculus, 9eChapter 2: Differentiation11) Let f(x) .Find all values of the real number k so that f is differentiable at x 1.A) -2 and 1B) 2 and -1C) -2 and 2D) only -2E) only 2Answer: DDiff: 312) There are lines that pass through the point (-1, 3) and are tangent to the curve xy 1. Findall their slopes.A) -1 and -9B) -1 and 9C) 1 and 9D) 1 and -9E) none of the aboveAnswer: ADiff: 22.4 The Chain Rule1) Find the derivative of.A)B)C)D)E)Answer: CDiff: 1Copyright 2018 Pearson Canada Inc.2-11

Calculus, 9eChapter 2: Differentiation2) Find the derivative of f(x) .A) B)C)D) E) Answer: ADiff: 13) Differentiate the following function: f(x) .A)B)C)D)E) none of the aboveAnswer: CDiff: 2Copyright 2018 Pearson Canada Inc.2-12

Calculus, 9eChapter 2: Differentiation4) Differentiate the following function: f(x) .A) 14B) -15C) -16D) 17E) 3Answer: BDiff: 25) Find an equation of the line tangent to the curve y A) 27x - y 28 0B) 27x y 26 0C) 27y - x - 28 0D) 27y x - 26 0E) 9x - y 10 0Answer: ADiff: 26) Use the values in the table below to evaluatex1-25f(x) (x)-261042-8at the point (-1, 1).(-2)g(x) (x)301508Answer: 30Diff: 27) Assuming all indicated derivatives exist, (A) (g(c)) (c)B) (c) g(c) f(c) (c)C) (c) (c)D) (c) (c)E) ( (c))Answer: ADiff: 1(c) is equal toCopyright 2018 Pearson Canada Inc.2-13

Calculus, 9eChapter 2: Differentiation8) Let f(x) (x - 2)(horizontal.A)andB) 4x - 7). Find all the points on this curve where the tangent line isandC)andD)andE)Answer: DDiff: 29) Find. Simplify your answer.A)B)C)D) E)Answer: CDiff: 210) Where does the function f(x) A) f(x) is differentiable everywhere.B) at x 0C) at x 1D) at x 0 and x 1E) none of the aboveAnswer: CDiff: 211) True or False: The function f(x) fail to be differentiable?is differentiable at x 0.Answer: TRUEDiff: 2Copyright 2018 Pearson Canada Inc.2-14

Calculus, 9eChapter 2: Differentiation2.5 Derivatives of Trigonometric Functions1) Differentiate y sin 4x.A) 2cos 4xB) 4cos 2xC) -4cos 4xD) 4cos 4xE) cos 4xAnswer: DDiff: 12) Find the derivative of y tan(cos( )).A)(-sin(2x))B) 2x cos( )C)(-2x sin( ))D)( ) cos( ) - tan( ) sin( )E) -2x(cos( )) sin( )Answer: EDiff: 23) Find the derivative of f(t) A) 15(5t) sin(5t)B) -3(5t) sin(5t)C) -15(5t) sin(5t)D) 15(5t)E) 3(5t)Answer: CDiff: 1(5t).4) Differentiatesin 2x.A) sin 2x cos 2xB)sin 2x cos 2xC) 3 sin 2x - 2 cos 2xD)sin 2x 2 cos 2xE) 3 cos(2x)Answer: DDiff: 1Copyright 2018 Pearson Canada Inc.2-15

Calculus, 9eChapter 2: Differentiation5) If cot(x), find (x).Answer: By chain rule (sin(x)) cos(x).Therefore we obtain:(sin(x)) cos(x) cot(x). It follows thatand hence(sin(x)) (sin(x)) . But. Now replacing sin(x) by x , we obtain (x)) .Diff: 26) Find the derivative of y tan( ).A) x( )B) 4x)C) 2x)D) 2x sec( ) tan( )E)( )Answer: CDiff: 27) Find the derivative of the following function: y A) -2sin xB) 2sin xC) -2sin xD) -2sin xE) -2tan(x)cos(x)sin(x)Answer: ADiff: 28) Let y . A simplified expression for(cos x).is given byA)B)C) D) - sin(x) -(x)E)Answer: CDiff: 2Copyright 2018 Pearson Canada Inc.2-16

Calculus, 9eChapter 2: Differentiation9) Find the slope of the curve y cosat the point where x .A) B) C) D) E) The slope is not defined at x .Answer: ADiff: 210) Find all points in the interval [0, π] where the curve y 2tangent line.A)andB)andC)andD)x - sin(2x) has a horizontalandE) The tangent line is never horizontal.Answer: ADiff: 32.6 Higher-Order Derivatives1) Find if y A) 12B) 5C) 15D) 20E) 10Answer: DDiff: 1.Copyright 2018 Pearson Canada Inc.2-17

Calculus, 9eChapter 2: Differentiation2) Find the second derivative of g(x) .A) (t) 2B) (t) - 3C) (t) 3D) (t) -2E) (t) 4Answer: CDiff: 13) True or False: Assuming all indicated derivatives exist,(x).Answer: TRUEDiff: 24) Find(2) given that - 7.A) 12B) 0C) 6D) 5E) 10Answer: ADiff: 15) let y , x 0. Show thatAnswer: First observe that the expression 324Indeed 324y 216 0 - 96 126 .is a perfect square., hence we have It follows that y 144 Therefore , since x 0.orandy 144 48 288 .Diff: 3Copyright 2018 Pearson Canada Inc.2-18

Calculus, 9eChapter 2: Differentiation6) Calculate the third derivative of f(x) A) -2sin(2x)B) -4sin(2x)C) -2cos(2x)D) -4sin xE) -2(x)Answer: BDiff: 27) Find a formula for the nth derivativeA) B) -C) D) E) x.of the function y .Answer: ADiff: 38) Find the second derivative of the function f(x) A) - B) -- C) - -D) E) .-Answer: ADiff: 2Copyright 2018 Pearson Canada Inc.2-19

Calculus, 9eChapter 2: Differentiation9) Find the second derivative of the function f(x) A) - 6x sin(2x) 8 cos(2x) - 4 sin(2x)B) 6x sin(2x) 8 cos(2x) - 4 sin(2x)C) 6x sin(2x) 12 cos(2x) - 4 sin(2x)D) - 6x sin(2x) 12 cos(2x) 4 sin(2x)E) 6x sin(2x) 12 cos(2x) 4 sin(2x)Answer: CDiff: 3sin(2x).10) Find the second derivative of the function f(x) .A) 1B) xC) D) E) 0Answer: ADiff: 22.7 Using Differentials and Derivatives1) A spherical balloon is being inflated. Find the rate of change of volume with respect to theradius when the radius is 5 cm.A) 200π/cmB) 100π/cmC) 300π/cmD) 400π/cmE) 500π/cmAnswer: BDiff: 12) Find the rate of change of the volume of a cube with respect to its edge length x when x 4 m.A) 40 /mB) 42 /mC) 48 /mD) 50 /mE) 8 /mAnswer: CDiff: 1Copyright 2018 Pearson Canada Inc.2-20