Indeterminate Powers and Products
Find the limits in Exercises 53–68.
57. lim (x → 0⁺) x^(-1/ln x)

Evaluate the integrals in Exercises 97–110.

107. ∫₀⁹ (2 log₁₀(x + 1) / (x + 1)) dx

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.

117. y = (√t)ᵗ

Evaluate the integrals in Exercises 97–110.

105. ∫₀² (log₂(x + 2) / (x + 2)) dx

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

8. y = ln kx, k constant

Evaluate the integrals in Exercises 53–76.

59. ∫(from 0 to 1)4ds/√(4-s²)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

35. y=arccsc(e^t)