Evaluate the integrals in Exercises 53–76.
65. ∫3dr/√(1-4(r-1)²)

Each of Exercises 25–36 gives a formula for a function y=f(x). In each case, find f^(-1)(x) and identify the domain and range of f^(-1). As a check, show that f(f^(-1)(x))=f^(-1)(f(x))=x.

f(x) = (x + 3) / (x − 2)

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

37. y=s√(1-s²) + arccos(s)

90. Find f'(0) for 

f(x) = e^(-1/x²), x≠0

   = 0, x = 0.

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.

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

13. y = 6sinh(x/3)