In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.
37. ∫(from x²/2 to x²)ln(√t)dt

Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)

13. lim(x → 1⁻)arcsin(x)

Evaluate the integrals in Exercises 91–102.

102. ∫(from -1/3 to 1/√3)(cos(arctan 3x))/(1+9x²) dx

Suppose that the range of g lies in the domain of f so that the composition fog is defined. If f and g are one-to-one, can anything be said about fog? Give reasons for your answer.

Each of Exercises 19–24 gives a formula for a function y=f(x) and shows the graphs of f and f^(-1). Find a formula for f^(-1) in each case.

f(x)=(x+1)², x≥-1

In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then evaluate the limit using a method studied in Chapter 2.

5. lim (x → 0) (1 - cos x) / x²

Use l’Hôpital’s rule to find the limits in Exercises 7–52.

49. lim (x → 0) (x - sin x) / (x tan x)