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# Review Sheet for MATH 1432 with Professor Morgan at UH

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Date Created: 02/06/15
Math 1432 Final Exam Review Graph the following and give the domain and range for fx a f x e b fx ln x C fx arcsinx d fx coshx For each of the parts for problem 1 find f x and Ifxdx Give the equation of the tangent line to the given graph at the point where X 0 a fx ln6x l e b fx 1n2x 1 364 c fx W Find the inverse of the following ifpossible 2 a fx 3x x1 b foc x2 Find the derivative of the inverse for the following a fx x3 1 f2 9 f 1399 b f3 1 f1 2 f 3 3 f 1 2 f 1 1 c fx passes through the points 3 2 and 2 1 The slope of the tangent line to the graph of fx atX 3 is 14 Evaluate the derivative of the inverse off at 2 5 The graph of x is shown below and di 42 7 x a 1 b 7271 and 7212 Gwe 3911 quot71 x 7 51mple tanarcsm3x for 0 lt x lt13 s Fmdthe largest Interval containing 2 on whxchthe function x 7 9x2 24x is mvernble lt2 Fmdthe equation ofthetangent andthe normal lmes tothe parametric Curves atthe gwen points a m 7205 22yt 4 2 724 b m 3cos3t 2yt15131 10 Gwe an equation relatingxandyforthe Curve gwen parame39cncally by a m 7713mst ytl25mt b m 713205ht yz125mht c xt7142 y 23equot lllntegrate a Icosh3xsmh2xdx I WSW dz 1smhx 1 Ex 2 n39 smx 50520311 Ide f 43 n g j 2 sinh5xdx J sin3x 16 cos2 3x 6x i dx J 4 x4 j Itan3xdx k J arctanx dx 1x2 J arctan3x 1 9x2 1 m dx J4x2 n IV9 x2dx o j31n4xdx p Ixze dx J 5x14 x1x2 4 J x25xz2 dx x1x 1 s I 2x2 dx V9 x2 t 12 arctan10xdx u 13x cos2xdx 12 A culture of bacteria is growing in such a way that the number of bacteria is changing at a rate proportional to the number ofbacteria If there are initially 10000 bacteria and 12000 bacteria are present siX hours later what is the doubling time for the culture give your answer in terms of In 13 Give the solution to 3y y0 2 x 14 Identify the geometric shape given by the parameterization xt 2 3 cost yt 1 3 sint 15 Give a parameterization for the line segment from the point 16 to the point 31 16 Give a parameterization for the curve given in polar coordinates by r 1 sint9 17 Give the formula for the arc length ofa curve parameterized by xt cost yt t2 forOStsl 18 Write the line y x in polar coordinates 4 19 Use long division to rewrite 3 2 x x 1 2x1 20 Give the partial fraction decomposition for 2 x 1 x2 1 21 Give the greatest lower bound of the set x x2 3x 10 lt 0 22 Does the sequence converge or diverge 2n2 1 3713 4n2 6 b39 mica 23 Give the limit of the sequence a n sin1n b till 24 Give the exact value of 25 Determine if the following series A converge absolutely B converge conditionally or C diverge w1n1J a Z n3 quot1 no b 20087271 2 n1 7 1 4n 1 cz MW 34quot 39 quot0 3n2 2n1 3n 1quot we 372 2n1 g i 2 1 zarctan n no n 2 lnn 2 quot2 n1i 1quot k 3n2 no W 2 1 Z 1 10m quot0 3quot 1quot n g n2 3n 2 039 i cos7mnquot n2 7 1 p39 quot111W 26 State the indeterminate form and compute the following limits a mum 4 new n2 1 E b in c 1im 1 Mac n d m x sin2x VH0 x s1n2x ex 1 e 11m 2 xrgt0 2x f lim Xigt0 x 3em 3x g 1123 x2 2 h limx Hoolnx 1x e 1 11m gt0 xe 1 j lim arctan4x xrgt0 x 27 Give the derivative of each power series below n 1x Z We 712 2 xn 2n1 bi 710 28 For each of the problems in number 27 give the antiderivate F of the power series so that F00 anl x 29 Suppose fx Give the 13th derivative off atX 0 n0 30 Give the 5th degree Taylor polynomial for ex centered at 0 31 Give the 6th degree Taylor polynomial for cosx centered at 0 32 Give the Taylor series expansion for fx equot centered at 0 33 Give a power series expansion for fx1nx centered at 1 34 Give a power series expansion for fx sin3x centered at 0 35 Give a power series expansion for fx centered at 0 1 1 x2 36 Find the smallest value of n so that the nth degree Taylor Polynomial for fx1n1 x centered at x 0 approximates 1n2 with an error ofno more than 0001 also be able to do this with some of the other Taylor Polynomials 37 f1 1 f 1 2f 1 1 Give the 2 101 degree Taylor polynomial forfcentered at 1 38 Rewrite fx x3 2x2 x1 in powers of x1 39 Evaluate each improper integral a ZJZerS 0 4 1 b 1 4 x 1 c jimdx 40 Find the formula for the area of r 1 2 sin 0 a Inside inner loop b Inside outer loop but outside inner loop c Inside outer loop and below XaXis 41 Find the radius of convergence and interval of convergence for the following Power series no x2n1 8139 Emu 1 n b 2706 1 quot0 3 no 1n1xn c Ell 4 d i 1quotxquotn 9 EM8 N X E 42 Give a power series representation for arctan2xand give the radius of convergence 43 Give a value ofn so that the Taylor polynomial of degree n for fx sinx centered at 0 can be used to approximate fx within 10 4 on the interval P 44 Use logarithmic differentiation to find the derivative of a y 3x 1sin b y x 1 quotltgt 1 c yx2 2 1 45 Determine the convergence 0r divergence for each series with the given general term Series Converge 0r Diverge Test used

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