Calculus I, Fall 2013 (http://www.math.nthu.edu.tw/˜ wangwc/)

Brief answer to selected problems in Homework 08

1. Section 4.4: The last problem should be problem 111, not problem 11. See the textbook for solutions.

2. Section 4.5: problem 80: a = −2, b = 0. problem 84(c): Answer = 1. problem 86: Solve for \frac{d}{dx}x^{\frac{1}{x^{n}}} = 0, one gets \frac{d}{dx} \frac{ln x}{x^{n}} = 0. So the only critical point is x = \frac{1}{n}. Next show that x = \frac{1}{n} is indeed a maximum by first derivative test. Answer: Maximum = e^{\frac{1}{ne}}.

3. Section 4.6: problem 12: maximize V (y) = \frac{1}{3}π(9 − y^{2})(3 + y) on 0 ≤ y ≤ 3. It is easier to calculate than using V (x).

problem 48: Similar to Example 4. Minimize t = \frac{\sqrt{a^{2} + x^{2}}}{c} + \frac{\sqrt{b^{2} + (d − x)^{2}}}{c} with respect to x, problem 60: Check (a) by direct differentiation. Similar for (b).