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)

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)

Evaluate the integrals in Exercises 53–76.

65. ∫3dr/√(1-4(r-1)²)

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 5–8, show that each function is a solution of the given initial value problem.

7. Differential Equation: xy' + y = -sin(x), x>0

Initial condition: y(π/2) = 0

Solution candidate: y = cos(x)/x

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

13. y = 6sinh(x/3)