Calculus I, Fall 2014 (http://www.math.nthu.edu.tw/~wangwc/)

Brief answer to selected problems in Homework 10

1. Section 5.4: Problems 84: Use L’Hôpital’s rule to get the limit. Answer = 2. Problems 89: F (x) = ∫_{1}^{x^{2}} \sqrt{1 − t^{2}}dt. F′(x) = 2x\sqrt{1 − (x^{2})^{2}}. F′′(x) = \frac{2(1−3x^{4})}{\sqrt{1−x^{4}}}.

2. Section 5.5: problem 79: All three are correct. One can also verify using trigonometric identities cos^{2} θ = 1 − sin^{2} θ = \frac{1+cos 2θ}{2}.