Solve the initial value problems in Exercises 115–120.
115. dy/dx = 1/√(1 - x²), y(0) = 0

Evaluate the integrals in Exercises 33–54.

∫(e^(3x) + 5e^(-x)) dx

Evaluate the integrals in Exercises 33–54.

∫ (e^(1/x) / x²) dx

In Exercises 25–36, find the derivative of y with respect to the appropriate variable.

33. y = csch⁻¹(1/2)^θ

In Exercises 57–70, use logarithmic differentiation to find the derivative of y with respect to the given independent variable.

70. y = ∛(x(x+1)(x-2)/(x²+1)(2x+3))

Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)

19. lim(x→∞)arccsc(x)

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

9. lim (t → -3) (t³ - 4t + 15) / (t² - t - 12)