126. Show that the sum arctan(x)+arctan(1/x) is constant.

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

1. lim (x → -2) (x + 2) / (x² - 4)

Evaluate the integrals in Exercises 33–54.

∫(e^(3x) + 5e^(-x)) dx

For problems 49–52 use implicit differentiation to find dy/dx at the given point P.

49. 3arctan(x) + arcsin(y) = π/4; P(1, -1)

73. Find the area between the curves y=ln(x) and y=ln(2x) from x=1 to x=5.

Evaluate the integrals in Exercises 53–76.

73. ∫(from 0 to ln√3) e^x dx/(1+e^(2x))

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

9. lim (t → -3) (t³ - 4t + 15) / (t² - t - 12)