Deck 6: Inverse Functions

Question 1

Find the limit.

A)
B)
C) 2
D)
E)0

Answer 1

Question 2

The integrals and are called Fresnel integrals. They are used to explain the phenomenon of light diffraction.Evaluate the given limit.

Answer 2

1/6

Question 3

Find the given integral.

Answer 3

Question 4

Find the limit.

A)5
B)
C)0
D)
E)

Question 5

At what point of the curve does the tangent line have slope ?

A)
B)
C)
D)
E)

Question 6

A painting in an art gallery has height h and is hung so that lower edge is a distance d above the eye of an observer (as in the figure). How far from the wall should the observer stand to get the best view? (In other words, where should the observer stand so as to maximize the angle subtended at his eye by the painting?)

A)
B)
C)
D)
E)

Question 7

Find the value of the expression accurate to four decimal places. cosh 2

A)3.3811
B)5.6269
C)8.5244
D)3.7622

Question 8

Evaluate the limit using l'Hôpital's Rule.

A)6
B)12
C)
D)4

Question 9

Find the derivative of the function. f(x) = sinh 4x

A)-sinh 4x
B)-4 cosh 4x
C)4 cosh 4x
D)4 sinh 4x

Question 10

Find the derivative of the function.
f (x) = sinh ^-1 6x

Question 11

Use the definitions of the hyperbolic functions to find the following limit.

A)
B)
C)
D)
E)None of these

Question 12

A telephone line hangs between two poles at 12 m apart in the shape of the catenary , where x and y are measured in meters. Find the slope of this curve where it meets the right pole.

A)
B)
C)
D) sinh 6
E)

Question 13

Find the limit , if it exists.

Question 14

Use l'Hospital's Rule to calculate the exact value of the limit as

A)
B)
C)
D)
E)0

Question 15

Find the derivative of the function.

A)
B)
C)
D)
E)None of these

Question 16

Find the derivative of the function. f (t) = cosh²(6t² + 3)

A)12t cosh (6t² + 3) sinh (6t² + 3)
B)24t sinh (6t² + 3)
C)24t cosh (6t² + 3) sinh (6t² + 3)
D)12t sinh (6t² + 3)

Question 17

Find the given integral.

A)9sinh (9x + 5) + C
B)sinh (9x + 5)+ C
C) sinh (9x + 5) + C
D)-sinh (9x + 5)+ C

Question 18

Find the derivative of y.

A)
B)
C)
D)
E)

Question 19

Find the limit , if it exists.

Question 20

Find the derivative of the function. y =

A)
B)
C)
D)

Question 21

Find the derivative of the function. y = (4x² + 1) tan^-1 2x

A)
B)4x² tan^-1 2x + 2
C)
D)8x tan^-1 2x + 2

Question 22

A lighthouse is located on a small island, km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?

A)
B)
C)
D)
E)

Question 23

Find

A)
B)
C)
D)
E)none of these

Question 24

Evaluate the integral.

A)
B)
C)
D)
E)

Question 25

Find .

A)
B)
C)
D)
E)

Question 26

Find the exact value of the given expression. sin^-1

A)
B) $\pi$
C)
D)2 $\pi$

Question 27

Evaluate the integral.

A)
B)
C)
D)
E)

Question 28

Find the derivative of

Question 29

Write the expression in algebraic form.
sec(sin^-1 8x)

Question 30

Evaluate the integral.

A)
B)
C)
D)
E)none of these

Question 31

Find the derivative of the function.
f (x) = 6 tan^-1 x²

Question 32

Evaluate the given integral.

A)
B)
C)
D)

Question 33

Strontium- has a half-life of days. A sample has a mass of mg initially. Find the mass remaining after 38 days.

A)
B)
C)
D)
E)

Question 34

Find the given integral.

Question 35

A curve passes through the point and has the property that the slope of the curve at every point is twice the -coordinate of . What is the equation of the curve?

A)
B)
C)
D)
E)

Question 36

If , find .

A)
B)
C)
D)
E)

Question 37

Strontium- has a half-life of days. A sample has a mass of mg initially. Find a formula for the mass remaining after days.

A)
B)
C)
D)
E)

Question 38

The half-life of cesium-137 is 30 years. Suppose we have a -mg sample. Find the mass that remains after years.

A)
B)
C)
D)
E)

Question 39

Find the exact value of the given expression. sin

A)
B)
C)0
D)1

Question 40

If $ is invested at 5% interest, find the value of the investment at the end of 5 years if the interest is compounded annually.

A)
B)
C)
D)
E)

Question 41

Differentiate the function.

A)
B)
C)
D)
E)

Question 42

Use logarithmic differentiation to find the derivative of the function.

A)
B)
C)
D)
E)

Question 43

Differentiate the function.

Question 44

Write the expression as an exponent with base

A)e ^{(tan 6x)}
B)e ^{(tan x) (ln 6)}
C)e ^{(6 tan x)}
D)6e ^{(tan x)}
E)6 ^{tan x}

Question 45

Differentiate the function. g(x) =

A)
B)
C)
D)

Question 46

Evaluate the integral.

Question 47

Find an equation of the line tangent to the graph of y = 6^x + 4 at the point (0, 5).

A)y = (ln 6)x + 4
B)y = 6x + 5
C)y = 6x + 4
D)y = (ln 6)x + 5

Question 48

Find, correct to three decimal places the area of the region above the hyperbola , below the x axis, and between the lines x = - 4 and x = - 3.

Question 49

Differentiate the function. y = x(7^2x)

A)[1 + (2 ln 7)x]7^2x
B)[1 + (7 ln 2)x]7^2x
C)(2 ln 7)7^2x
D)(2 ln 7)(7^2x)x

Question 50

Evaluate the integral to three decimal places.

A)0.533
B)0.094
C)0.194
D)0.183
E)

Question 51

Differentiate the function.

Question 52

Use logarithmic differentiation to find the derivative of the function.

Question 53

Differentiate the function.

Question 54

Differentiate the function.

A)
B)
C)
D)
E)

Question 55

Use logarithmic differentiation to find the derivative of the function.

Question 56

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. f (x) = 0.5x³ - 1.7x² + 2.3x - 2; g (x) = 2.8x - 4.8

A)(-1.21519, -8.20253), (3.15415, 4.03163)
B)(-1.21519, -8.20253), (1.46104, -0.7091)
(3)15415, 4.03163)
C)(-1.21519, -3.40253) (1.46104, 8.83163)
(3)15415, 4.0909)
D)(-1.21519, -3.40253) (3.15415, 4.0909)

Question 57

Differentiate the function.

Question 58

Evaluate the expression. log₁₂₅ 25

A)
B)
C)
D)

Question 59

Use logarithmic differentiation to find the derivative of the function.

Question 60

Find

Question 61

Evaluate the integral.

Question 62

Simplify the expression. e ^{3 ln 2}

A)9
B)5
C)6
D)8

Question 63

Use the properties of logarithms to expand the quantity.

Question 64

Use transformations to sketch the graph of the function.

Question 65

Find the limit.

A)
B)
C)
D)
E)

Question 66

Find the limit.

A)
B)
C)
D)
E)

Question 67

The geologist C. F. Richter defined the magnitude of an earthquake to be where I is the intensity of the quake (measured by the amplitude of a seismograph 100 km from the epicenter) and S is the intensity of a "standard" earthquake (where the amplitude is only cm). The 1989 Loma Prieta earthquake that shook San Francisco had a magnitude of on the Richter scale. The 1906 San Francisco earthquake was times as intense. What was its magnitude on the Richter scale?

A)
B)
C)
D)
E)

Question 68

Use logarithmic differentiation to find the derivative of the function.
y = (x + 7)^5/x

Question 69

Solve the equation. 2e ^{x + 5} = 4

A)x = ln - 5
B)x = ln + 5
C)x = ln + 5
D)x = ln - 5

Question 70

Solve the inequality.

A)
B)
C)
D)
E)

Question 71

Find the limit.

A)
B)
C)
D)
E)

Question 72

Express the quantity as a single logarithm.

A)
B)
C)
D)
E)none of these

Question 73

Find the work done by the force (measured in pounds) in moving an object along the x-axis from to . (x is measured in feet.)

Question 74

Find the limit.

A)
B)
C)
D)
E)

Question 75

Find the integral.

Question 76

Use the properties of logarithms to expand the quantity.

A)
B)
C)
D)
E)

Question 77

Suppose that the graph of is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches ft.

A) mi
B) mi
C) mi
D) mi
E) mi

Question 78

Find the domain of the function. f (x) = ln (8x + 7)

A)
B)
C)
D)

Question 79

Find the limit.

A)0
B)
C)
D)

Question 80

Differentiate the function. y = e ^{cos 3x}

A)-e ^{cos 3x} sin 3x
B)-3e ^{cos 3x} sin 3x
C)-3e ^{cos 3x} sin x
D)e ^{cos 3x} sin 3x