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


14. lim (t → 0) sin 5t / 2t

Evaluate the integrals in Exercises 87–96.

89. ∫₀¹ 2^(−θ) dθ

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

51. y arccos(xy) = -3√2/4 π; P(1/2, -√2)

L’Hôpital’s Rule

Find the limits in Exercises 103–110.

105. lim(x→∞) x arctan(2/x)

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

19. lim (θ → π/6) (sin θ - 1/2) / (θ - π/6)

Evaluate the integrals in Exercises 97–110.

101. ∫ (log₁₀x / x) dx

Suppose that the differentiable function y = f(x) has an inverse and that the graph of f passes through the point (2, 4) and has a slope of 1/3 there. Find the value of df⁻¹/dx at x = 4.