132. Let f(x) = e^x / (1 + e^(2x)).
b. Find all inflection points for f.

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)

Evaluate the integrals in Exercises 67–74 in terms of

b. natural logarithms.

71. ∫(from 1/5 to 3/13)dx/(x√(1-16x²))

9. True, or false? As x→∞,

c. x = O(x+5)

Evaluate the integrals in Exercises 67–74 in terms of

b. natural logarithms.

67. ∫(from 0 to 2√3)dx/√(4+x²)

Verify the integration formulas in Exercises 37–40.

37. b. ∫sech(x)dx = sin⁻¹(tanh x) + C

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