2. Which of the following functions grow faster than e^x as x→∞? Which grow at the same rate as e^x? Which grow slower?
e. e^(-x)

1. Express the following logarithms in terms of ln 2 and ln 3.

d. ln ∛9

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

e. x^3 - x^2

112. True, or false? Give reasons for your answers.

e. sec^(-1)x = O(1)

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

e. x ln(x)

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:

d. Find the equation for the tangent line to g at the point (f(x_0), x_0) located symmetrically across the 45° line y=x (which is the graph of the identity function). Use Theorem 1 to find the slope of this tangent line.

72. y= 2-x-x³, -2 ≤ x ≤ 2, x_0 = 3/2

6. Which of the following functions grow faster than ln(x) as x→∞? Which grow at the same rate as ln(x)? Which grow slower?

e. x - 2ln(x)