Chapter 6 Practice Test Flashcards Preview

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Flashcards in Chapter 6 Practice Test Deck (20):
1

Given x^ 2 − y^ 2 = 1, find dy / dx by implicit differentiation.

dy/dx=x/y

2

Given xy = 5, find dy / dx by implicit differentiation.

−y / x

3

Given √x+1/√y=1, find dy/dx by implicit differentiation.

√y^3/x

4

Given cos (x + y) = sin x sin y, find dy / dx by implicit differentiation.

−sin(x+y)+cosxsiny/sin(x+y)+sinxcosy

5

Evaluate the following as true or false. If dx/dy=1/dydx=0,then the tangent line to the curve y=f(x) is horizontal.

false

6

Find all points on the curve y + x = x^ 2 + y^2 where the tangent line is horizontal.

(1/2,1+√2/2) and (1/2,1−√2/2)

7

Find all points on the curve ln (xy) = x^ 2 where the tangent lines are vertical.

None of the tangent lines are vertical.

8

Which of the following functions is its own inverse? In other words, for which of the following functions is f −1 (x) = f (x)?

f (x) = 1 / x

9

What is the inverse of f(x)=3 3√x+1/5?

f−1(x)=(5x−1/3)^3

10

What is the value of d/dx[f−1(x)] when x=2, given that f(x)=2x−4?

1/2

11

What is the value of d/dx(f−1(x)) when x=7/3, given that f(x)=x^5+1/3x^3+x and f−1(7/3)=1?

1/7

12

What is the value of d/dx[f−1(x)] when x=π, given that f(x)=2x+cos^2x and f−1(π)=π/2?

1/2

13

What does arcsin(√3/2) equal?

π / 3

14

What does arcsin (sin (5π / 4)) equal?

−π / 4

15

Solve the equation arccos (x ^2 − 2x + 2) = 0 for x.

x = 1

16

What is the largest interval containing x = 2π on which sin x is one-to-one?

[3π / 2, 5π / 2]

17

Find the derivative d/dx[arctan(x^2+1)]

2x/1+(x^2+1)^2

18

Find the derivative d/dx[2arcsin(x−1)].

2/√−x^2+2x

19

Find the derivative of y=l/n(tanhx/2)

csch x

20

Find the derivative of f(x)=xcoshx−sinhx

x sinh x

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