Complete the following steps for the given function interval, and value of \( n \). a. Sketch the graph of the function on the given interval. b. Calculate \( \Delta x \) and the grid points \( x_{0} x_{1} \quad x_{n} \) c. Illustrate the left and right Riemann sums, and determine which Riemann sum underestimates and which sum overestimates the area under the curve d. Calculate the left and right Riemann sums. \[ f(x)=\cos (x-5 \pi / 8) \text { on }[\pi / 2 \pi] n=4 \]

Set up the definite integral required to find the area of the region between the graph of \( y=16-x^{2} \) and \( y=-2 x-47 \) over the interval \( -3 \leq x \leq 7 \).

Evaluate the \( \lim _{x \rightarrow-2}\left(\frac{x^{3}+6 x^{2}+8 x}{x+2}\right) \) Solution:

A factory selling cell phones has a marginal cost function \( C(x)=0.01 x^{2}-3 x+229 \), where \( x \) represents the number of cell phones, and a marginal revenue function given by \( R(x)=429-2 x \). Find the area between the graphs of these curves and \( x=0 \).

Sketch the region enclosed by \( y=e^{2 x}, y=e^{4 x} \), and \( x=1 \). Find the area of the region.

\( \int \sqrt[ \infty ] { x ^ { r } } d x \)