Evaluate the integrals in Exercises 33–54.
∫₀^(π/4) (1 + e^(tan θ)) sec²θ dθ

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

32. lim (x → 0) (3^x - 1) / (2^x - 1)

In Exercises 7–10, determine from its graph if the function is one-to-one.

f(x) = 3 - x, x < 0

= 3, x ≥ 0

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

41. lim (x → 0⁺) (ln x)² / ln(sin x)

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

9. (sinh(x)+cosh(x))⁴

In Exercises 59–86, find the derivative of y with respect to the given independent variable.

65. y = (cos θ)^(√2)

Solve the differential equation in Exercises 9–22.

15. √x (dy/dx) = e^(y+√x), x > 0