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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 L’Hospital’s 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
 LYLES
 Derivative, Limit of a function, Exponentiation, Convex function

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