If $ f(x) = x + \sqrt{2-x} $ and $ g(u) = u + \sqrt{2-u} $, is it true that $ f = g $?

The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds.

The velocity function (in meters per second) is given for a particle moving along a line. Find (a) the displacement and (b) the distance traveled by the particle during the given time interval.

$ v(t) = 3t - 5 $, $ 0 \le t \le 3 $

A rectangular storage container with an open top is to have a volume of $ 10 m^3 $. The length of its base is twice the width. Material for the base costs \$ 10 per square meter. Material for the sides costs \$ 6 per square meter. Find the costs of materials for the cheapest such container.

Find the Taylor series for $ f(x) $ centered at the given value of $ a. $ [Assume that $ f $ has a power series expansion. Do not show that $ R_n (x) \to 0.$] Also find the associated radius of convergence.

$ f(x) = \sin x, $ $ a = \pi $

The directed line segment $\overset{\rightharpoonup} {\small PQ}$ has ________ point $\small P$ and ________ point $\small Q$.