80. Find all values of c that satisfy the conclusion of Cauchy's Mean Value Theorem for the given functions and interval.
b. f(x) = x, g(x) = x², (a, b) arbitrary

91. [Technology Exercise] 91. The continuous extension of to (sin x)^x to [0, π]

b. Verify your conclusion in part (a) by finding lim(x→0⁺)f(x) with l’Hôpital’s Rule.

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

8. b. arccot(√3)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

2. b. tan^(-1)(√3)

Suppose that the function f and its derivative with respect to x have the following values at x=0, 1, 2, 3, and 4.

Assuming the inverse function f^(-1) is differentiable, find the slope of f^(-1)(x) at

b. x=2

75. b. Identify the function’s local and absolute extreme values, if any, saying where they occur.

g(x) = x(ln x)²

Find the volumes of the solids in Exercises 135 and 136.

135. The solid lies between planes perpendicular to the x-axis at x=-1 and x=1. The cross-sections perpendicular to the x-axis are

b. vertical squares whose base edges run from the curve y=-1/√(1+x²) to the curve y=1/√(1+x²).