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:
c. Find the equation for the tangent line to f at the specified point (x_0, f(x_0)).
68. y= (3x+2)/(2x-11), -2 ≤ x ≤ 2, x_0=1/2

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?

c. √x

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

7. c. arcsec(-2)

c. Find the slopes of the tangent lines to the graphs of f and g at (1, 1) and (−1, −1) (four tangent lines in all).

10. True, or false? As x→∞,

c. 1/x - 1/x² = o(1/x)

In Exercises 41–44:

c. Evaluate df/dx at x = a and df⁻¹/dx at x = f(a) to show that

(df⁻¹/dx)|ₓ₌f(a) = 1 / (df/dx)|ₓ₌a

44. f(x) = 2x², x ≥ 0, a = 5

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?

c. ln(√x)