Suppose that the function g and its derivative with respect to x have the following values at x=0, 1, 2, 3, and 4.
Assuming the inverse function g^(-1) is differentiable, find the slope of g^(-1)(x) at
a. x=1

84.a. Find the center of mass of a thin plate of constant density covering the region between the curve y=1/√x and the x-axis from x=1 to x=16.

4. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?

a. x² + √x

In Exercises 41–44:

a. Find f⁻¹(x).

41. f(x) = 2x + 3, a = −1

Evaluate the integrals in Exercises 67–74 in terms of

a. inverse hyperbolic functions.

67. ∫(from 0 to 2√3)dx/√(4+x²)

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

7. a. sec^(-1)(-√2)

143.

a. Show that ∫ ln(x) dx = x ln(x) − x + C.