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)).


72. y= 2-x-x³, -2 ≤ x ≤ 2, x_0 = 3/2

Evaluate the integrals in Exercises 67–74 in terms of

b. natural logarithms.

69. ∫(from 5/4 to 2)dx/(1-x²)

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

c. √(x^4 + x^3)

132. Let f(x) = e^x / (1 + e^(2x)).

b. Find all inflection points for f.

9. True, or false? As x→∞,

c. x = O(x+5)

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

5. c. arccos(√3/2)

Evaluate the integrals in Exercises 67–74 in terms of

b. natural logarithms.

67. ∫(from 0 to 2√3)dx/√(4+x²)