Use l’Hôpital’s rule to find the limits in Exercises 7–52.
24. lim (x → π/2) (ln(csc x)) / (x - (π/2))²

Evaluate the integrals in Exercises 77–90.

79. ∫(from -1 to 0)6dt/√(3-2t-t²)

Solve the initial value problems in Exercises 115–120.

117. dy/dx = 1/(x√(x² - 1)), x > 1; y(2) = π

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.

y = xe^x-e^x

Evaluate the integrals in Exercises 91–102.

96. ∫dy/((arcsin y)(1-y²))

22. The function ln x grows slower than any polynomial Show that ln(x) grows slower as x→∞ than any nonconstant polynomial.

In Exercises 1–4, show that each function y=f(x) is a solution of the accompanying differential equation.

3. y = 1/x ∫(from 1 to x) e^t/t dt, x²y' + xy = e^x