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practice2 - Exam 2(MODIFIED for 2009 M175-004 Spring 2004...

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Unformatted text preview: Exam 2 (MODIFIED for 2009) M175-004 Spring, 2004 Name: (1 pt.) 1. (15 pts.) Find the antiderivative. Show all steps. I need to know that your are doing the work, not your calculator. xe2x dx 2. (15 pts.) Find the antiderivative. Show all steps. I need to know that your are doing the work, not your calculator. x2 √ dx 4 − x2 3. (15 pts.) Find the antiderivative. Show all steps. I need to know that you are doing the work, not your calculator. x+1 dx x2 − 2x 4. (15 pts.) Find n so that the error in a Trapezoid approximation to √ π sin(x2 ) dx 0 is no more than 0.0001. 5. (20 pts.) Determine if each of the following is convergent or divergent. Reasons are not required, but I will give no partial credit for a wrong answer with no reason. ∞ (a) 2 ∞ (b) 0 ∞ (c) 1 ∞ (d) 1 ∞ (e) 1 x2 + 3x − 1 dx x4 + 2x 3x 2x+2 x ln x + 2 dx x3 + x2 2x xx x(ln x)5 dx ex 6. (10 pts.) Find a so that ∞ a dx < 0.01 x(ln x)3 1 7. (10 pts.) Use the information below to approximate ∞ 1 ln x + x dx ex with an error no greater than 0.002. f (x) = ln x + x ex 2 3 4 5 2 Graph of the second derivative of 3 4 5 0 –0.2 –0.4 –0.6 –0.8 –1 –1.2 –1.4 Graph of the fourth derivative of f (x) = ln x + x ex 0 –2 –4 –6 –8 –10 2 ...
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practice2 - Exam 2(MODIFIED for 2009 M175-004 Spring 2004...

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