Day26c_Night_1432FinalComplete

L i m x 3e x 3 3 x x 0 x2 h l i m x l n x x2 i

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Unformatted text preview: . lim x →0 e x2 −1 2x 2 ⎛1⎞ f. l i m ⎜ ⎟ x →0 + ⎝ x ⎠ g. l i m x 3e x / 3 − ( 3 + x ) x →0 x2 h. l i m x →∞ l n x x2 i. l i m x →0 j. l i m x →0 1 + x − ex ( x ex −1 ) a r ct a n ( 4 x ) x 2. Give the exact value of ∞ 1 ∑ 2n . n= 0 3. Give the exact value of ∞ ∑ 1 . n ( n + 1) ∞ cos ( πn ) n= 2 4. Give the exact value of ∑ n= 2 n 3 . 5. Evaluate each improper integral, and explain why it is improper. Use correct notation. a. b. ∫ ∫ 2 −1 1 dx 2 x 1 06 1 1− x dx c. d. ∫ 7 5 27 ∫ 0 14 ( x −6 ) x − 2 / 3 dx 2 dx 4 e. f. 1 ∫ 4−x 0 ∫ ∞ 0 dx 1 dx = 2 1+ x g. ∫ 5 dx 2 x −2 = Notes for series “growth”: Let p(k) be a polynomial in k. rk for r > 1 grows much faster than p(k) k! grows much faster than rk, p(k) kk grows much faster than the others Hence, ∑ ∑ p (k ) r k rk , k! , ∑ ∑ p (k ) k! , rk , k k ALL converge rapidly. ∑ ∑ p (k ) kk k! kk Determine if the following series converge absolutely, converge conditionally, or diverge...
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This note was uploaded on 02/01/2014 for the course MATH 1432 taught by Professor Morgan during the Spring '08 term at University of Houston.

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