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Chapter 3: Q 5. (page 298)
Give formulas for the volume and the surface area of a cylinder whose radius is half of its height .
Volume of cylinder is.
Surface area of cylinder is.
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Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of and examine any relevant limits so that you can describe all key points and behaviors of f.
For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.
Sketch the graph of a function f with the following properties:
f is continuous and defined on R;
f(0) = 5;
f(鈭�2) = 鈭�3 and f '(鈭�2) = 0;
f '(1) does not exist;
f' is positive only on (鈭�2, 1).
For each graph of f in Exercises 49鈥�52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.
For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.
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