[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)

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.

145. The linearization of eˣ at x = 0

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

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

a. x² + 4x

Find the volumes of the solids in Exercises 135 and 136.

135. The solid lies between planes perpendicular to the x-axis at x=-1 and x=1. The cross-sections perpendicular to the x-axis are

a. circles whose diameters stretch from the curve y=-1/√(1+x²) to the curve y=1/√(1+x²).