145. The linearization of eˣ at x = 0
a. Derive the linear approximation eˣ ≈ 1 + x at x = 0.

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))

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

1. a. arctan 1

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.

75. a. Find the open intervals on which the function is increasing and decreasing.

g(x) = x(ln x)²

[Technology Exercise] In Exercises 139–141, find the domain and range of each composite function. Then graph the compositions on separate screens. Do the graphs make sense in each case? Give reasons for your answers. Comment on any differences you see.

139. a. y=arctan(tan x)