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This 5 page Class Notes was uploaded by Alvena McDermott on Saturday September 19, 2015. The Class Notes belongs to MATH 1432 at University of Houston taught by Pamela Balthazar in Fall. Since its upload, it has received 35 views. For similar materials see /class/208376/math-1432-university-of-houston in Mathmatics at University of Houston.
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Date Created: 09/19/15
MATH 1432 Review Problems Exam 2 Due 10 30 09 NAME Recitation Inst ruct or Part I Techniques of Integration 1 1 d Answer z2x1 7 z2 I 1 2 7 dz Answer z4 7 16 z2 8z 7 3 3 dz Answer 4 I d Answer 7 z x4 z2 1 I2 5 0 m dz Answer 2 2 7 4 6 dz Answer z3 7 4z Part II Numerical Integration Set z2 1 on 04 4 1 Use the midpoint rule with n 4 to approximate dz 0 Answer 4 2 Use the trapezoidal rule with n 4 to approximate dz 0 Answer 4 3 Use Simpsonls rule with n 2 to approximate dz 0 Answer 4 Determine the smallest integer n such that the t 39 39 quot Tn 39 4 l dz with error less than 00075 0 Answer 2 5 Determine the error if 54 is used to estimate ex dz Use e m 3 0 Answer Part III Polar Coordinates 1 Give the rectangular coordinates of the point with polar coordinates 72 87r3 Answer 2 Give all possible polar coordinates for the point with rectangular coordinates 74 7 4 Answer 3 Sketchthegraphof7quotl2cost97 039347r3 Answer The graphs of C1 7 2 7 cos 9 and C2 7 1 cos 9 are shown in the gure 4 Calculate the area of the region inside C2 and outside C1 Answer 5 Calculate the area of the region common to C1 and C2 Answer 6 Find the polar equation for I2 y22 41y Answer Write the equation 7 4 sin 9 in rectangular coordinates 7 Answer Part IV Parametric Equations 1 Express the curve I 2 sin t y 71 Cos t by an equation in z and y Answer 2 Find a parametrization of the line segment from 72 3 to 17 5 Answer 3 Find a parametrization for the curve y3 12 from 11 to 87 4 Answer 4 Give an equation for the normal line to the graph of z sin t y 2 cos 2t at the point where t 7r6 Answer 5 Give an equation for the line tangent to the polar curve 7 200s 9 at the point where 9 7r3 Answer 6 Find the points 17y at which the curve I t2 7 2t y t3 7 372 St has a a horizontal tangent7 b a vertical tangent Answer a Answer b 7 Findthelengthofthecurve C zt21 yt3737 0 t 2 Answer 8 Find the length of the polar curve 7 1 7 cos 9 0 S 9 S 27L Answer 9 Find the length of the graph of 232 0 g I g 2 Answer 10 A particle moves along the curve I t3 7 t y t2 2 0 g t g 2 a What is the speed of the particle at time t b What is the total distance traveled by the particle Answer m Answer b Part IV Sequences 1 Determine a formula for an the general term of the given sequence Then determine whether the sequence converges and if it does7 give the limit 1 1 2 3 2 4 3 5 4 a 471717E7 5 T7 lt gt 7 lt gt 7 ltZgt 7 Answer m Answer b 2 Determine whether or not the given sequence is bounded above7 bounded below7 bounded If it is bounded above or below7 give the least upper andor greatest lower bounds a cosltm3gt b lt6 l2l Answer m Answer b Answer c 3 Determine the monotonicity of the given sequence a 03 b C n2 n Answer m Answer b Answer c 4 Determine whether or not the given sequence converges or diverges If it converges7 give the limit a b C Answer m Answer b Answer c
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