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# Sheet6 - Math 21B Kouba Challenge Sheet 6 1 SET UP the...

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Unformatted text preview: Math 21B Kouba Challenge Sheet 6 1.) SET UP the partial fractions decomposition for each rational function. DO NOT SOLVE for the unknown constants. a)3:3+zv2+:1:+3 b) 700 C):135+:1:—100 ' 124—1 . m3(\$2+5)3 ' 178—1 2.) Use any method to integrate the following. a.)/;(721:ﬁdx b.)/x—(;;—§1:——ﬁdzc c.) f—l— da: d.) /(m—1)\/ﬂ dm \$1/2 _ 373/2 e.) / x/ar——l m d1: f.) g.)/x-de h.)/\/mdm i.) /\/1_1——:I:E (13: j.) /\/zv2—+4 d3: k.)/m.mdm 1.)/\$7.¢16.—\$4dx 3.) Derive recursion formulas for each integral (n is a positive integer and b is a constant). a.) fx'lsinbx da: b.) /cot"sc dx 4.) You are standing with an empty pail at point A, 3 miles from a road and 5 miles from a river. You must walk to the river, ﬁll the pail with water, return the pail to the road, then walk back to point B on the river. Determine the shortest possible walking distance required to complete this task. A 3 Road ——————————¢—— RlVeY‘ t——--—————-— \a,—————--—-————-i ...
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