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)

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

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

7. a. sec^(-1)(-√2)

In Exercises 67–72, you will explore some functions and their inverses together with their derivatives and tangent line approximations at specified points. Perform the following steps using your CAS:

a. Plot the function y=f(x) together with its derivative over the given interval. Explain why you know that f is one-to-one over the interval.

72. y= 2-x-x³, -2 ≤ x ≤ 2, x_0 = 3/2

Evaluate the integrals in Exercises 67–74 in terms of

a. inverse hyperbolic functions.

69. ∫(from 5/4 to 2)dx/(1-x²)