75. a. Find the open intervals on which the function is increasing and decreasing.
g(x) = x(ln x)²

82. Use the definitions of the hyperbolic functions to find each of the following limits.

a. lim(x→∞) tanh x

Evaluate the integrals in Exercises 67–74 in terms of

a. inverse hyperbolic functions.

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

In Exercises 1–4, solve for t.

1. a. e^(-0.3t) = 27

153. The linearization of 2ˣ

a. Find the linearization of f(x) = 2ˣ at x = 0. Then round its coefficients to two decimal places.

145. The linearization of eˣ at x = 0

a. Derive the linear approximation eˣ ≈ 1 + x at x = 0.

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?

a. x-3