111S08_Final

# Final exam 592008 2 question 1 3 points each total 15

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Final Exam (5/9/2008) 2 Question 1. (3 points each, total 15 points) (*Limits*) Compute the following limits. Be sure to show your work. (a) lim x →∞ x 3 + 2 x + 7 ( x 2 - 1)(2 x + 3) (b) lim x 0 sin x x (c) lim x →∞ sin x x (d) lim x →∞ x sin parenleftbigg 1 x parenrightbigg (e) lim h 0 sin ( π 3 + h ) - sin( π 3 ) h Question 2. (4 points each, total 16 points) (* Derivatives*) integraldisplay x 1 2 t dt Question 3. (5 points each, total 15 points) (*Antiderivatives and integration*) integraldisplay ln3 ln2 e x ( e x + 1) 2 dx integraldisplay sin 5 ( x ) cos 4 ( x ) dx

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Math 111 (Spring 2008) Final Exam (5/9/2008) 3 Question 4. (3 points each, total 15 points) (*True/False*). If true, explain why. If false, give an explicit example for which the statement is false. integraldisplay f ( x ) g ( x ) dx = parenleftbiggintegraldisplay f ( x ) dx parenrightbigg parenleftbiggintegraldisplay g ( x ) dx parenrightbigg integraldisplay b a x 4 dx = b 3 - 3 - a 3 - 3
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• Fall '06
• MARTIN,C.
• 5/9/2008

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