241fine - Calculus I (Math 241) Final Problem 1. [16...

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Calculus I (Math 241) – Final Problem 1. [16 Points] Calculate the derivatives of the following functions: f ( x ) = sin 3 (2 x - 5) g ( x ) = r 1 + sec(2 x ) , h ( x ) = sin(2 x ) tan(3 x ) , t ( x ) = R 1 + x 1 - x . Problem 2. [16 Points] Calculate the integrals: i x ( x - 1) π dx, i sec 2 x tan 2 x dx, i dt 16 + t 2 , i π 3 0 sin 2 x dx. Problem 3. [20 Points] Discuss the function f ( x ) = x 3 - 2 x 2 - 3 x. SpeciFcally, address the following: 1. ±ind the intercepts and the intervals on which the function is positive, resp., negative. 2. ±ind the critical points and the intervals on which the function is in- creasing, resp., decreasing. 3. ±ind the intervals on which the function is concave up, resp., concave down. 4. ±ind the local maxima and minima and the in²ection points. 5. Sketch the graph in accordance with the information obtained above. Problem 4. [14 Points] Use Frst principles to Fnd f ( a ) if f ( x ) = x 4 .
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This note was uploaded on 07/26/2009 for the course MATH 215 taught by Professor Heiner during the Spring '09 term at Hawaii.

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241fine - Calculus I (Math 241) Final Problem 1. [16...

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