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# Note for MATH 1431 with Professor George at UH test 2 review with answer

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Date Created: 02/06/15

Math 1431 Exam 2 Review Find the following limits if they exist a 11mm i e lim x 27ljj 39 z7gto 5x 5 z7gto x v4xi2 39 2sinxcosx hmi f l1rn7 I me x i zrgt0 2x 1 1 1 5 Ernier l g lirn x f z7gto x z7gto Lang 7 2 7 v 2 111117quot X if h 11mm 0 x7 X 9 0 x7gto 6x Determine ifthe following are continuous lfthe function is not continuous state the type ofcliscontinuity x2l xltl a fx 8 xl Uoj jump x3 xgtl 2x1 xlt2 b fx8 x2 3 5 x3 xgt2 57x xlt72 I c fx 7 F72 011 x175 xgt72 x1 ifxlt7l d fx 5 x2 ifxzil x1 ifx 3 Letfx k ifx3 For what value of kwoulcl X be continuous at X5 Find A and B so that X is continuous 6x1 71 x lt 71 A 5 fx A x7l E Bx3 x gt71 5 Given f 7 2quot 03 find f393 ifit exists D U I x 7 x1 73 x53 39 I 6 Find the derivative ofthe following a fx32x44 0 10 2413103 ysec3lt2x 539 A Samba tan 2y 5 I c fx3 1 Xi 1 L d fX plba a 3 A e fxV2X g39 y 4X5 I X f fxx2 2x ltx71f Cm y axquot 339Jrl quotk b VX R 5U Hh x ltlx1 g fltxgt quot W 3 0 W 2 Ix nsx h 1 x x3 5x I 1cosx 3 a 5 1 5mquot 139 fXlCOSx 410 I msgx l fxSiHA4JC2 6x1 Pl z lim alytkwu 1550M ka 3 k 00th 3 I y ud y 1y cotX I x2 x l l ft9sect97tan0 f 8 Sens tune secl 7 Find 1 using implicit differentiation Fr ewenesva x2y274x3y7 A3539 XH sinxicosy720 34 Dj cmxcscj xjixyy31 33 J 33quotquot on 5 13593 ywEix il6 Axilg uq xy10 e 3 t xsin2y 1 v A j A5 23 23 3 x y 75 glj xy k 339 quotSln 43 l y 5me 53 cosx y 4xy 8 Use differentials to approximate a M 2 1 39339 b cos31 2 4339 117300 9 Use the definition ofderivative to find the derivative of the following 3 fJC3JC2 7x 2 TA A beam the mm I 2 make sur Lieu use comet b39 fxm notatum c form 3 10 Finddiz 3x472x3x710 8 ix 4 11 Find Xlat x72 for y4xllix3 339lt 2 37 12 Find the second derivative at the point 21 for x2 7 y2 3 393 13 Use interval notation to give the solution set to a x2xil3x450 00 43 U 0 7 b x177x6gt0 quotIlUbm i i 2 14 F1nd Em 5dx2x x may I 15 Aparticle is moving along the parabola yi 4X2 As it passes through the point 7 6 its y coordinate is increasing at the rate of3 units per second How fast is the Xcoordinate changing at this instant 7 u n I39hrg 16 A man is standing on the top ofa 15 footladder which is leaning against a wall Some scientific minded joker comes up and starts to pull thebottom ofthe ladder away at a steady rate of 6 ftmin At what rate is the man on the ladder descending ifhe remains standing on the top rung when the bottom ofthe ladder is 9 ft from the wall 9A itm damn the Mn 17 Apoint moves along the curve y 2x2 1 in such awaythattheyvalue is decreasing at the rate of 2 units per second At what rate is X changing when X 37 quot V3 Um39tjsec 2 18 On a morningofa day when the sun will pass directly overhead the shadow ofan 40ft building on level ground is 30 feet long At the moment in question the angle the sun makes with the ground is increasing at the rate of ISOO radiansminute Athtt39thhdl hd 397 w a ra e1s es a ow engt greasmg 3171 mn 19 Write the equation ofthe tangent and normal line to a y2 7x60atthepoint 153 b 2x2 76xy y2 9 at the point 151 no 71 5 3 720 15 h 1133 005 quotL yaruxm NL 31 20 Find the critical numbers offand classify the extreme values given x e 31 fx 4 of may I 14 x 4 Lbs n139n391n h 21 Find all local extreme and intervals of increas ing and drec39reasing ogl mquot fx x376x2 tn 90 I U l I a 3 dzcr a IrElsa low M C39 4116 22 Use the intermediate value theorem to show that the function fx 2x5 3x1 has a root on the interval 712 Lani 413 41m quot1 41m 7 LL047 has a fact 23 Suppose we are given the data in the table about the functionsfandg and their derivatives Find the following values X 1 2 3 4 fx 3 2 1 4 f x 1 4 2 3 g x 2 1 4 3 g39x 4 2 3 1 a h4 if hxfgx 17 h394 if hxfgx 6 h4 if hxgfx l a 3 d h394 if hxgfx 8 h394 if hx f h394 if hxfxgx 3 3 la 24 Use the plot ofthe function onthe interval 23 to give a geometric depiction of the mean value theorem 25 Let fx 5 73x be defined on 11 Find con 1 1 that satisfies the conclusion ofthe Mean Value Theorem 395 i 0quot a

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