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


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

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

Evaluate the integrals in Exercises 33–54.

∫ (e^(1/x) / x²) dx

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

19. lim(x→∞)arccsc(x)

Solve the initial value problems in Exercises 115–120.

115. dy/dx = 1/√(1 - x²), y(0) = 0