In Exercises 41–44:
a. Find f⁻¹(x).


43. f(x) = 5 − 4x, a = 1/2

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)

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

a. ln secθ + ln cosθ

Verify the integration formulas in Exercises 37–40.

37. a. ∫sech(x)dx = tan⁻¹(sinh x) + C

10. True, or false? As x→∞,

a. 1/(x+3) = O(1/x)

In Exercises 41–44:

a. Find f⁻¹(x).

44. f(x) = 2x², x ≥ 0, a = 5