Evaluate the integrals in Exercises 31–78.
58. ∫(from 0 to ln9)e^θ(e^θ-1)^(1/2) dθ

In Exercises 129–132 solve the initial value problem.

131. x dy - (y + √y)dx = 0, y(1) = 1

110. Does f grow faster, slower, or at the same rate as g as x→∞? Give reasons for your answers.

f. f(x) = sech(x), g(x) = e^(-x)

Use l’Hôpital’s Rule to find the limits in Exercises 85–108.

85. lim(x→1) (x² + 3x - 4)/(x - 1)

Evaluate the integrals in Exercises 31–78.

77. ∫dt/((t+1)√(t²+2t-8))

Use l’Hôpital’s Rule to find the limits in Exercises 85–108.

91. lim(x→π/2⁻) (sec(7x))(cos(3x))

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

7. y = log₂(x²/2)