Quiz 3: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Evaluate the limit using l'Hôpital's Rule. A)75 B)25 C)15 D)

Evaluate the limit using l'Hôpital's Rule. A) B)3 C)0 D)

Find the limit. A) B)0 C) D)1 E)

Evaluate the limit using l'Hôpital's Rule. A)0 B)1 C) D)e

Find the limit.

Find the numerical value of the expression. A) B) C) D) E)

Find the value of the expression accurate to four decimal places.sinh 4 A)29.3082 C)15.145 B)55.5798 D)27.2899

Find the numerical value of the expression. A) B) C) D) E)

Find the derivative. A) B) C) D) E)

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) E)

Find the exact value of the expression. A) B) C) D) E)

Find the exact value of the expression. A) B) C) D) E)

Simplify the expression. A) B) C) D) E)

Find the derivative of the function. Simplify where possible. A) B) C) D) E)

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)

The half-life of cesium is years. Suppose we have a -mg sample. Find the mass that remains after years. A) B) C) D) E)

The half-life of cesium- is years. Suppose we have a -mg sample. How much of the sample remains after years? A) B) C) D) E)

If is invested at interest, find the value of the investment at the end of years if the interest is compounded . A) B) C) D) E)

If is invested at interest, find the value of the investment at the end of years if the interest is compounded . A) B) C) D) E)

Differentiate the function. A) B) C) D)

Use logarithmic differentiation to find the derivative of the function. A) B) C) D)

Use logarithmic differentiation to find the derivative of the function. A) B) C) D) E)

If , find . A) B) C) D) E)

Find . A) B) C) D) E)

Differentiate the function.

Differentiate the function.

Find an equation of the tangent line to the curve at .

Find a formula for the inverse of the function. A) B) C) D) E)

Find the exact value of the expression. A)2 B)4 C)1 D)5 E)3

Use the laws of logarithms to expand the expression.ln A) ln B) ln (x + 5) - ln (x - 6) C) ln [(x + 5)(x - 6)] D) ln

Use the laws of logarithms to write the expression as the logarithm of a single quantity.4 ln 5 - ln (x + 6) A) B) C) D)

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 3 ft? Rounded to the nearest mile. A)13,014,952 mi B)13015052.4 mi C)5.2 mi D)13,015,152 mi E)1084587.7 mi

Solve the equation. A)x = ln + 2 B)x = ln - 2 C)x = ln + 2 D)x = ln - 2

When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by (The maximum charge capacity is and t is measured in seconds.) How long does it take to recharge the capacitor to 90% of capacity if ? A) seconds B) seconds C) seconds D) seconds E) seconds

Find the domain, range, and x-intercept(s) of the function.

Solve each equation for x.(a) (b)

Determine whether f is one-to-one.

The graph of f is given. Sketch the graph of on the same set of axes. 3

Starting with the graph of , write the equation of the graph that results from shifting 5 units right. A) B) C) D) E)

Starting with the graph of , find the equation of the graph that results from reflecting about the line . A) B) C) D) E)

Find the exponential function whose graph is given. A) B) C) D) E)

Find the limit. A) B) C) D) E)

Find the limit. A) B) C) D) E)