ReviewSheet-Midterm2[UnknownDate]

ReviewSheet-Midterm2[UnknownDate] - MTH 104 Review Exam 2...

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MTH 104 / Review Exam 2 Q1. Evaluate the following integrals: a) dx x x 3 1 b) 0 2 2 2 u u du c) dx x x x x 3 4 4 2 2 3 d) 0 1 2 ) tan 1 )( 1 ( y y dy e) dx x x 10 3 ) 1 ( f ) 1 0 2 2 1 dt t t t Q2. For each of the following improper integrals determine whether it converges or diverges. a) 1 dx x e x b) dx x x 2 sin 1 c) 0 3 6 1 1 dt t t Q3. Find the volume of the solid obtained by rotating about the y-axis the region under the curve 4 1 1 x y from 0 x to x . Q4. For each of the following sequences determine whether it converges or diverges. If it convergence, find its limit. a) n n n a 2 b) ) 2 sin( n b n c) n n n c 10 9 1 d) ) 4 ( 3 1 , 1 1 1 n n a a a . Show that {a n } is increasing and bounded above by 2 Q5. Find the sum of the following series: a) ) 1 1 1 ( 2 n n n b) 1 1 3 2 n n n c) 1 1 2 ) 5 2 ) 3 ( 1 ( n n n n n d) Express 1.2345345345… as fraction.
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  • Spring '14
  • KathrynLynch
  • English, Mathematical analysis, following improper integrals, following series, n 1 

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