Evaluate the integrals in Exercises 39–56.
47. ∫(from 2 to 4)dx/(x(ln x)²)

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

37. lim (y → 0) (√(5y + 25) - 5) / y

Theory and Applications

L’Hôpital’s Rule does not help with the limits in Exercises 69–76. 

Try it—you just keep on cycling. Find the limits some other way.

71. lim (x → (π/2)⁻) sec x / tan x

Evaluate the integrals in Exercises 41–60.

55. ∫(from -π/4 to π/4)cosh(tanθ)sec²θ dθ

In Exercises 57–70, use logarithmic differentiation to find the derivative of y with respect to the given independent variable.

66. y = θsin(θ)/√(sec(θ))

Evaluate the integrals in Exercises 77–90.

77. ∫dx/√(-x²+4x-3)

In Exercises 115–126, use logarithmic differentiation or the method in Example 6 to find the derivative of y with respect to the given independent variable.

120. y = x^(sin x)