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Unformatted text preview: ucsc econ/ams 11b Review Questions 4 Solutions 1. Compute the differentials of the functions below. a. y = x 2- 3 x + 1 , dy = (2 x- 3) dx b. u = e x 2- 3 x +1 , du = e x 2- 3 x +1 (2 x- 3) du 2. Use differentials to estimate 3 √ 28. Express your answer as a simple fraction, a/b , not in decimal form. We use the approximation formula f ( x + dx ) ≈ f ( x )+ dy . First, we identify the function, which is straightforward: f ( x ) = x 1 / 3 . Next, we identify x . We want to set 28 = x + dx , and we want dx to be relatively small, and we also want x to be a point for which it is easy to evaluate f ( x ). In other words we are looking for a point, x , that is close to 28 and for which the cube root is known. x = 27 fills the bill. So, we have f ( x ) = x 1 / 3 , x = 27 and dx = 28- 27 = 1. Next we compute dy : dy = f ( x ) dx = 1 3 x- 2 / 3 dx = 1 3 27- 2 / 3 · 1 = 1 27 . Finally, we plug everything back into the approximation formula, above....
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This note was uploaded on 09/16/2011 for the course ECON 11B taught by Professor Binici during the Spring '08 term at University of California, Santa Cruz.
- Spring '08