Solve the initial value problems in Exercises 87 and 88.
87. dy/dx = 1 + 1/x, y(1) = 3

90. Find f'(0) for 

f(x) = e^(-1/x²), x≠0

   = 0, x = 0.

Solve the differential equation in Exercises 9–22.

12. (dy/dx) = 3x²e^(-y)

Evaluate the integrals in Exercises 53–76.

71. ∫(from -π/2 to π/2) 2cosθ dθ/(1+(sinθ)²)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

29. y=arcsec(1/t), 0<t<1

Rewrite the expressions in Exercises 5–10 in terms of exponentials and simplify the results as much as you can.

8. cosh(3x) - sinh(3x)

82. Find a curve through the point (1, 0) whose length from x=1 to x=2 is

L = ∫(from 1 to 2)√(1 + 1/x²)dx.