Chapter 6 Practice Test Flashcards Preview

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

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

A

dy/dx=x/y

2
Q

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

A

−y / x

3
Q

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

A

√y^3/x

4
Q

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

A

−sin(x+y)+cosxsiny/sin(x+y)+sinxcosy

5
Q

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.

A

false

6
Q

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

A

(1/2,1+√2/2) and (1/2,1−√2/2)

7
Q

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

A

None of the tangent lines are vertical.

8
Q

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

A

f (x) = 1 / x

9
Q

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

A

f−1(x)=(5x−1/3)^3

10
Q

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

A

1/2

11
Q

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?

A

1/7

12
Q

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?

A

1/2

13
Q

What does arcsin(√3/2) equal?

A

π / 3

14
Q

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

A

−π / 4

15
Q

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

A

x = 1

16
Q

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

A

[3π / 2, 5π / 2]

17
Q

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

A

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

18
Q

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

A

2/√−x^2+2x

19
Q

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

A

csch x

20
Q

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

A

x sinh x

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