Use l’Hôpital’s Rule to find the limits in Exercises 85–108.
99. lim(x→0) (2^sin(x) - 1)/(e^x - 1)

Evaluate the integrals in Exercises 31–78.

31. ∫e^x sin(e^x)dx

Evaluate the integrals in Exercises 31–78.

49. ∫x3^(x²)dx

In Exercises 129–132 solve the initial value problem.

129. dy/dx = e^(-x-y-2), y(0) = -2

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

c. f(x) = 10x^3 + 2x^2, g(x) = e^x

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

11. y = 5x^(3.6)

Evaluate the integrals in Exercises 31–78.

61. ∫(from 1 to 3)(ln(v+1))²/(v+1) dv