150webfnl-062 - Math 150 FINAL EXAM Spring 2006[18 1 Find the following limits You must show all your work x2 8x 15 a lim 2 x3 x x 12 tan 3x b lim

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Math 150 – FINAL EXAM – Spring 2006 [18] 1. Find the following limits. You must show all your work. a) lim x 3 x 2 - 8 x +15 x 2 + x - 12 b) lim x 0 tan3 x x c) lim x →∞ ( x - x 2 - 2 x +5) [10] 2. USING THE DEFINITION of derivative ±nd the derivative of f ( x )= x - 2. [30] 3. Find f ± ( x ) for the following functions. You do not need to simplify your answers. a) f ( x e x - x + cot x b) f ( x )=( x 2 +5 x + 2)cosh x c) f ( x 1+ln x x + sin x d) f ( x x 2 +4 x - 1) 2 / 3 e) f ( x x sin x f) f ( x ± x 1 dt sin 2 t +1 [8] 4. Let y ( x ) be de±ned implicitly by x 3 +ln( x + y y . Find y ± ( x ). [12] 5. Determine an equation of the tangent line to the curve f ( x ) = ln( x - 1) at the point where the graph crosses the x -axis. [10] 6. The combined electrical resistance R of R 1 and R 2 , connected in parallel, is given by 1 R = 1 R 1 + 1 R 2 where R, R 1 and R 2 are measured in ohms. R 1 and R 2 are increasing at rates of 1 and 1.5 ohms per second, respectively. At what rate is R changing when R 1 = 50 ohms and R 2 = 75 ohms?
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This note was uploaded on 03/12/2012 for the course MATH 150 taught by Professor A during the Spring '05 term at University of Arizona- Tucson.

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150webfnl-062 - Math 150 FINAL EXAM Spring 2006[18 1 Find the following limits You must show all your work x2 8x 15 a lim 2 x3 x x 12 tan 3x b lim

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