In Exercises 25–36, find the derivative of y with respect to the appropriate variable.
31. y = cos⁻¹(x) - x sech⁻¹(x)

Use the results of Exercise 55 to show that the functions in Exercises 56–60 have inverses over their domains. Find a formula for df⁻¹/dx using Theorem 1.

f(x) = (1 − x)³

Use l’Hôpital’s rule to find the limits in Exercises 7–52.

30. lim (θ → 0) ((1/2)^θ - 1) / θ

Evaluate the integrals in Exercises 53–76.

53. ∫dx/√(9-x²)

Evaluate the integrals in Exercises 33–54.

49. ∫ e^(sec πt) sec πt tan πt dt

For Exercises 127 and 128 find a function f satisfying each equation.

128. f(x) = e² + ∫₁ˣ f(t) dt

Use l’Hôpital’s rule to find the limits in Exercises 7–52.

47. lim (t → ∞) (e^t + t²) / (e^t - t)