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:
e. Plot the functions f and g, the identity, the two tangent lines, and the line segment joining the points (x_0, f(x_0)) and (f(x_0), x_0). Discuss the symmetries you see across the main diagonal y=x.


72. y= 2-x-x³, -2 ≤ x ≤ 2, x_0 = 3/2

9. True, or false? As x→∞,

e. e^x = o(e^(2x))

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

f. (e^x)/2

1. 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. (3/2)^x

5. 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

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)

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)