Textbook Question
Evaluate the integrals in Exercises 97–110.
107. ∫₀⁹ (2 log₁₀(x + 1) / (x + 1)) dx
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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
Indeterminate Powers and Products
Find the limits in Exercises 53–68.
57. lim (x → 0⁺) x^(-1/ln x)
In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.
8. y = ln kx, k constant
In Exercises 21–48, find the derivative of y with respect to the appropriate variable.
35. y=arccsc(e^t)
Which of the functions graphed in Exercises 1–6 are one-to-one, and which are not?