Math%20119%202005-2006%20Fall%20MidTerm2

# Math%20119%202005-2006%20Fall%20MidTerm2 - METU Department...

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Muhiddin UĞUZ Last Name Name Student No. Department Section Signature : : : : : : : : : : : : : Code Acad. Year Semester Coordinator Date Time Duration M E T U Department of Mathematics CALCULUS I Mid Term 2 Math 119 2005-2006 Fall Muhiddin Uguz December.10.2005 09:00 120 minutes 6 QUESTIONS ON 6 PAGES TOTAL 60 POINTS 1 2 3 4 5 6 SHOW YOUR WORK Question 1 (4+2+4=10 points) Let f ( x ) = 3 x ( x - 1) be defined on [ - 1 , 1] . a) Find local extremas of f ( x ) b) Find the absolute extremas of f ( x ) c) Approximate f (0 , 98) by linearization

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Muhiddin UĞUZ Question 2 (4+4+4=12 points) Evaluate the limits. If you use a theorem or a well known limit, state it explicitly. a) lim n →∞ 1 n n k =1 ( k n ) 15 b) lim x 0 x 2 x sin( t ) t dt x c) lim x 0 2 x - 1 3 x - 1
Muhiddin UĞUZ Question 3 (4+4+4=12 points) Find the following integrals a) x 5 x 3 + 1 dx b) π 4 0 tan 3 ( x ) dx c) x 2 sin( x ) dx

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Muhiddin UĞUZ Question 4 (3+2+2+3=10 points) Let f ( x ) = x 2 x 2 - 1 a) Find all asymptotes of the graph of f ( x ) b) Find the intervals where f ( x ) is increasing and the intervals where f ( x ) is decreasing c) Find the intervals where

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