Math151FinalSols

# Math151FinalSols - SOLUTIONS TO THE FINAL MATH 151 SPRING...

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SOLUTIONS TO THE FINAL MATH 151 – SPRING 2004 – KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100% An appropriate sheet of notes and a scientific calculator are allowed. PART 1 45 POINTS TOTAL; 3 POINTS FOR EACH PROBLEM Give the best answers based on the notes and our discussions in class. 1) We would use a u -substitution to evaluate sin cos 45 xx d x Ú . What would be our choice for u ? ux = sin 2) We could use a trig substitution to evaluate x x dx 3 2 93 6 + Ú . What would we use as our trig substitution? 36 2 x x = = tan tan q , or 3) We want to find 1 25 32 2 dx + () Ú using partial fractions. Write the form of the partial fraction decomposition for the integrand, 1 25 2 + . A x B x C x Dx E x Fx G x +++ + + + + + 232 2 2 25 25 4) Find lim cos x x x Æ - - p 2 2 . Write or -• if appropriate. If the limit does not exist, and and are inappropriate, write “DNE” (Does Not Exist). Show work! lim cos lim sin x Æ - ¢ Æ - - Ê Ë Á ˆ ¯ ˜ = - =- pp 22 2 0 0 1 1 LH }

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5) Which of the following are indeterminate limit forms? Circle all that apply: •+• •-• 0 6) Fill in the boxes (there is more than one possible way): 2 3 2 3 2 3 2 3 2 3 4 3 4 3 4 4 4 3 4 4 4 4 x dx x dx x dx x dx x dx t t w w - () = - + - = - + - •• Æ ÚÚ Ú lim lim 7) For a series a n n = Â 1 , we know that the n th partial sum is given by S n n n = + - 31 23 2 2 . What must be the sum of the series? The sum of the series is given by lim n n S Æ• , if it exists.
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## This note was uploaded on 09/08/2011 for the course MATH 151 taught by Professor Bray during the Spring '07 term at Mesa CC.

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Math151FinalSols - SOLUTIONS TO THE FINAL MATH 151 SPRING...

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