241finc - Calculus I (Math 241) Final Problem 1. [12...

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Calculus I (Math 241) – Final Problem 1. [12 Points] Calculate the derivatives (do not simplify): d dx ( x 3 cos 2 (3 x + 1) ) and d dx b x 2 + 1 ( x 3 + x ) 4 B and d dx arctan( x 2 - sin x ) Problem 2. [12 Points] Calculate the integrals: i π/ 2 0 sin(3 x ) dx and i t ( t + 1) 9 dt and i x ( x 2 + 4) 2 dx. Problem 3. [6 Points] DeFne the concept of a limit . In other words, make precise the statement that L = lim x a f ( x ) for a given function f ( x ) and an interior point a of its domain. Problem 4. [12 Points] ±ind the equation of the tangent line to the function f ( x ) = x 4 - 7 x 2 at x = 1, and use approximation by di²erentials to Fnd an approximate value of f at x = 1 . 05. Problem 5. [24 Points] Consider a round box with top and bottom. Its interior is divided into quarters. It is made from S square centimeters of material. ±ind its height ( h ), radius ( r ), and the ratio h/r if its volume is maximal.
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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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241finc - Calculus I (Math 241) Final Problem 1. [12...

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