Exam 7: Logarithmic, Exponential, and Hyperbolic Functions

Solve the problem. -A BASE jumper's velocity (in meters per second) after t seconds is given by where m is the mass of the object in kilograms, g = 9.8 m/ s² is the acceleration due to gravity, and k is a physical constant. How fast is the BASE jumper falling at the end of a 12 second delay? Use m = 75kg and k = 0.2 Round the answer to one decimal place if necessary.

Evaluate the integral. - dx

Determine the indefinite integral. -

Find the derivative of y with respect to x, t, or θ, as appropriate -y = ln(ln 8x)

Use a calculator to evaluate the expression, or state that the value does not exist. Round the answer to four decimal places when necessary. -coth 2

Determine the indefinite integral. - , x > 4

Evaluate the definite integral. Express the answer in terms of natural logarithms. -

Compute dy/dx for the function. -y = sinh 7x

Evaluate the expression without using a calculator, or state that the value does not exist. Simplify the answer to the extent possible. -sinh(2 ln 4)

Evaluate the integral. - dx

Compute dy/dx for the function. -y = ln sinh 5x

Evaluate the derivative. -f(x) =

Evaluate the integral. -

Evaluate the integral. -

Evaluate the expression without using a calculator, or state that the value does not exist. Simplify the answer to the extent possible. -sech 0

Write the word or phrase that best completes each statement or answers the question. -Use the fundamental identity x - x = 1 to verify the identity. 1 - x = x

Evaluate the integral. -

Evaluate the expression without using a calculator, or state that the value does not exist. Simplify the answer to the extent possible. - (ln 7)

Determine the indefinite integral. -

Evaluate the integral. - d $\theta$