Decide if each of the following problems is a linearization problem, an optimization prob- lem, a related rates problem, a graphing problem, or a Newton's method problem. Identify. Label the problem...

Decide if each of the following problems is a linearization problem, an optimization prob-lem, a related rates problem, a graphing problem, or a Newton's method problem then do the steps it says.

Extracted text: Decide if each of the following problems is a linearization problem, an optimization prob- lem, a related rates problem, a graphing problem, or a Newton's method problem. Identify. Label the problem as one of the five types or explain that it is not exactly one of those types (and how you know). Begin solution. For each problem, start the solution. Linearization. State what function you would linearize and where you would linearize it. Optimization. Draw a diagram to define your variables. Write the function you would optimize, including the domain of the function. Related Rates. Draw a diagram to define your variables. Write an equation that relates your variables. Graphing. State the function, its domain, and any critical points in the domain. Newton's method. State the function to which you would apply Newton's method, your initial point, and the Newton iteration. Other. Explain how you might use calculus to solve this problem.


Extracted text: 1. The volume of a sphere is changing at 10 inches per second. How fast is the radius changing at the moment the radius is 7 inches? 2. Estimate a solution to In(r² + 5) = 1 using the tools of calculus. 3. Estimate arctan(0.998) using tools of calculus.