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Unformatted text preview: Math 21A
1 (40 pts.) Brian Osserman Practice Exam 2 Dierentiate the following functions. Show your work if you wish to receive partial credit. You do not need to simplify your answers. (a) f (x) =
3x+7 x4 +1 . (b) f (x) = x2 +1 tan-1 (x2 +1) . (c) f (x) = e2x-1 x + 1. (d) f (x) = sec2 (x + sin x). (e) f (x) = (ln x)10 . 2 (10 pts.) Suppose u(x) is a dierentiable function of x, and let f (x) = xu(x) , for
x > 0. Find f (x), in terms of x, u(x), and u (x). Hint: take the natural log of both sides and use implicit dierentiation. 3 (20 pts.) Consider the parametric curve (- t + 1, 3t). (a) Find the tangent line to the curve at the point corresponding to t = 3. (b) Find d2 y/(dx)2 at the same point. 2 4 (10 pts.) Find the equation of the line tangent to the curve dened implicitly by
2 sin-1 y = x2 at the point ( , 2 1 ) 2 . 5 (20 pts.) Consider the function
f (x) = x sin 1 : x = 0 x 0 : x=0 . (a) Is f (x) continuous at x = 0? Why or why not? (b) Is f (x) dierentiable at x = 0? Why or why not? If so, what is f (0)? 3 ...
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This note was uploaded on 10/07/2008 for the course MATH 21A taught by Professor Osserman during the Spring '07 term at UC Davis.
- Spring '07