MATH118MW04N

# MATH118MW04N - f 00 ( x ) | 1 2 on [0 , 24]. Recall: Error...

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MATH 118, Calculus 2, Midterm, Feb 11th, 2004 Note: Questions not relevant to this year’s test have been omitted. 1: Evaluate each of the following integrals: a) R cos 3 θ dθ b) R 1 4 - x 2 dx c) R arctan x dx d) R x x 2 +4 x +13 dx e) R x 3 ( x 2 +2) 2 dx 2: Given that R e x sin x dx = e x 2 (sin x - cos x )+ C and R e x cos x dx = e x 2 (sin x +cos x )+ C evaluate the deFnite integral R π/ 3 0 xe x sin x dx . 4: Given the table of values for y = f ( x ) below x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 y 4 5 4 3 2 2 2 3 4 5 6 3 2 1 1 2 4 4 4 3 1 1 3 4 7 a) Use Simpson’s Rule with 8 subdivisions to approximate R 24 0 f ( x ) dx b) Determine the number of equal subdivisions required to have an error less than 1 100 in approximating R 24 0 f ( x ) dx using the trapezoidal rule where |
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Unformatted text preview: f 00 ( x ) | 1 2 on [0 , 24]. Recall: Error M ( b-a ) 3 12 n 2 5) a) Sketch x = t-t 2 , y = t + t 2 ,-2 t 2 b) Determine the slope of the tangent line to the curve in part a) at t = 1. ANSWERS 1) a) sin x 3 (2 + cos 2 x ) + C b) 1 4 ln f f f z +2 z-2 f f f + C c) x arctan x-1 2 ln(1 + x 2 ) + C d) 1 2 ln( x 2 + 4 x + 13)-2 3 arctan x +2 2 + C e) 1 2 ln( x 2 + 2) + ( x 2 + 2)-1 + C 2) 6 e / 3 3-1 2 -e / 3 4 4) a) 71 b) 240 5)-3 1...
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## This note was uploaded on 02/06/2011 for the course MATH 118 taught by Professor Zhou during the Spring '08 term at Waterloo.

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