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Unformatted text preview: Final Exam MAT 17A Name: ID Number: Directions: Do not begin until instructed to do so. You may use pencils, pens, erasers, and calculators. Put away all books, notes, cell phones, or electronic devices. Turn off your cell phone. Show all work, clearly in order to receive full credit. I reserve the right to take off points if I cannot see how you arrived at your answer (even if your final answer is correct). Leave your answers in exact form unless otherwise instructed (i.e. 2 not 1.41). Circle or otherwise indicate your final answers. You must present your student ID when turning in your exam. This test has 10 problems and 17 pages (not including this page). Good luck! I pledge that I have not received unauthorized assistance on this exam. Signature: Name: 1. ( 12 points ) Evaluate the following limits. Show all work. Indicate if you use LHospitals Rule and the indeterminate form. ( a ) ( 2 points ) lim x 1 x 1 x 2 1 ( b ) ( 5 points ) lim x ( 1 + e 2 x ) 1 /x 1 Name: 1. continued. ( c ) ( 5 points ) lim x + 1 sin x 1 x 2. ( 12 points ) Compute the derivative of the following functions with respect to the indepen dent variable. Do not simplify your answer. ( a ) ( 2 points ) f ( x ) = x 4 + 4 x 2 Name: 2. continued. ( b ) ( 3 points ) f ( x ) = sin( e 2 x + x ) ( c ) ( 4 points ) f ( x ) = x 2 x ( d ) ( 3 points ) f ( x ) = ln(cos(1 x )) 3 Name: 3. ( 12 points ) Sketch the graph of f ( x ) that satisfies the following conditions.) that satisfies the following conditions....
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 Spring '08
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