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# Review Sheet for MATH 1432 with Professor Balthazar at UH

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This 6 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 14 views.

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Date Created: 02/06/15

4 Determine the smallest integer n such that the trapezoidal approximation Tn approximates 4 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 03947r3 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 4 Determine the smallest integer n such that the trapezoidal approximation Tn approximates 4 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 03947r3 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 7 Write the equation 7 4 sin 9 in rectangular coordinates 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 2cos 9 at the point where 97r3 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 zt2l yt3737 0 t 2 Answer 8 Find the length of the polar curve 7 1 7 cos 9 0 g 9 g 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 a 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 471717 7 5 T7 lt gt 7 lt gt 7 lt1gt 7 Answer a 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 cosn7r3 b C 2 77371 Answer a Answer b Answer c 3 Determine the monotonicity of the given sequence a 03 b C n2 Answer a Answer b Answer c 4 Determine whether or not the given sequence converges or divergesi If it converges7 give the limit Answer a Answer b Answer c MATH 1432 Review Problems Exam 2 Due 10 30 09 NAME Recitation Instructor Part I Techniques of Integration 1 1 dz Answer z2x1 7 z2 1 2 7 dz Answer z4 7 16 2 8 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 Ldz 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

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