23. What roles do the functions e^x and ln(x) play in growth comparisons?

Evaluate the integrals in Exercises 31–78.

45. ∫(ln x)^(-3)/x dx

80. Find all values of c that satisfy the conclusion of Cauchy's Mean Value Theorem for the given functions and interval.

a. f(x) = x, g(x) = x², (a, b) = (-2, 0)

5. Which of the following functions grow faster than ln(x) as x→∞? Which grow at the same rate as ln(x)? Which grow slower?

a. log_3(x)

In Exercises 1–24, find the derivative of y with respect to the appropriate variable.

1. y = 10e^(-x/5)

4. Use the properties of logarithms to write the expressions in Exercises 3 and 4 as a single term.

a. ln secθ + ln cosθ

In Exercises 79–84, solve for y.

83. ln(y-1) = x + ln(y)