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M151groupfinalS02

M151groupfinalS02 - Last Name Name Instructor Math 151...

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Last Name: Name: Instructor: Math 151 Group Final (Spring 2002) You are not allowed to use notes, books or calculators . You have two hours . S imp l i fyyourresponsesasmuchasposs ib le . Points 1. 2. 3. 4. 5.
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In problems 1 3 , compute the required inde f nite integral. 1 (8 pts.) Z x cos (5 x ) dx 2 (7 pts. ) Z cos 2 ( x )sin 3 ( x ) dx 2
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3 (8 pts.) Z x 19 ( x 3) ( x +1) dx 3
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4 (10 pts.) Determine whether the improper integral Z 0 −∞ xe x dx converges or diverges, and its value in case it converges. 4
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5. Consider the improper integral Z 2 0 x x 2 4 dx a) (3 pts.) Why is the integral an improper integral? b) (8 pts.) Determine whether the improper integral converges or di- verges, and its value in case it converges. 5
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(7 pts.) Use the ratio test to determine whether the in f nite series X n =1 ( 1) n n ! 10 n converges absolutely or diverges. 7
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M151groupfinalS02 - Last Name Name Instructor Math 151...

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