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Unformatted text preview: 1 Practice exercises for Exam 2 Please remember that if there are homework problems or in-class examples that you have not understood you would be better off revisiting them first. 1. Implicit differentiation: (a) Differentiate implicitly e xy = y x (b) Find the equation of the tangent line to the curve y = x- 2 y + 1 through the point where y = 1 2. A parametric curve is described by equations x ( t ) = t 3 + 1 y ( t ) = ln( t- 1) Find y and dy dx when x = 9 in two different ways: (a) Directly without determining the cartesian equation for the function y ( x ). (b) By computing and differentiating the cartesian equation. Hint: first, solve for t from the equation for x , and plug it into the expression for y . 3. Use linearization to approximate the following: (a) 1 3 . 9 (b) (sin0 . 01 + cos0 . 01) 2 4. The graph of the derivative f ( x ) is shown on the picture. Where is the original function f ( x ) increasing or decreasing? Concave up, concave down? Identify its extrema. Where are the inflection points? 2 5. Suppose g ( x ) is a continuous...
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This note was uploaded on 11/30/2010 for the course BIOS 101 taught by Professor Plantz during the Spring '08 term at UNL.
- Spring '08