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MAT295-2007Spring - F IN AL E XAM M AT 2 95 N ame May 7 2...

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MAT 295 FIN AL EXAM - May 7, 2007 Name: _ Signature: _ Instructor: (please circle one) P. CARNEY J. DATTA J. DEEGAN H.DOERR P KIMANI A. MURPHY A. ORENSTEIN L. SHEN Read before you begin: 1. This exam contains 10 problems for a total of 160 points. There are 9 pages including the cover sheet. You are responsible for checking that they are all present. 2. You must show all work to completely justify your answers in order to receive any credit. Unsupported answers will receive little or no credit. Problem Points 1. 15 2. 15 3. 20 4. 10 5. 10 6. 10 7. 16 8. 16 9. 24 10. 24 Total 160 1
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Math 295 FIN AL EXAM - May 7, 2007 1. (1S points) Find the following limits, if they exist. Justify your answer completely. You may NOT use L'Hospital's Rule for this problem. 3 (a) lim 2x - 3x + 1 :1:-->+00 4x 3 + 7 x - 4 (b) lim sin(x) :1:-->0 x cos( x) (c) lim x + 1 :1:-->-2+ x 2(x + 2) 2
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2. (15 points) Find the following limits. (a) lim 1 - cos x X-+O x 2 + X (b) lim xtan(l/x) x-+oo (c) lim(l - 2x )l/x x-+O 3
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3. (20 points) Find the indicated derivatives.
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