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Calculus I

by: Alvena McDermott

Calculus I MATH 1431

Alvena McDermott
GPA 3.69

Rebecca George

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Rebecca George
Class Notes
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This 7 page Class Notes was uploaded by Alvena McDermott on Saturday September 19, 2015. The Class Notes belongs to MATH 1431 at University of Houston taught by Rebecca George in Fall. Since its upload, it has received 66 views. For similar materials see /class/208381/math-1431-university-of-houston in Mathmatics at University of Houston.


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Date Created: 09/19/15
Math 1431 Exam 3 Review 1 Find the critical numbers offand classify the extreme values given X Er31 x x 7 f x2 4 2 Find all quot intervals m 39 39 39 the following functions a fx x3 76x2 h f0 xgSiHI F cos for 0 S S 27 3 Each ofthe graphs below are graphs off Determine wheref is increasing decreasing intervals of concave up and concave down List all local maximum and minimums and points ofin ection 4 The value Xa is a critical numher forfX Classify a as a local maximum local minimum or neit er a f 3 712XZX8 1 3 h x7x x377x27x4x1 f 4 2 Evaluate e a ifelf34t n d 2 b 7 3tr4t m V dzidz 1 i 41 C 11x gr 276 Gwen the graph affix d m n Fm The area ofthe regon bounded by fix and the xraxls between 72 and 4 I nd 2 7 Considerthe function fx3x 720x342x2 r36x onthemtewal 04 m a Showthatthe crmcal numbers off are 1 and 3 b Gwethe mtervale ofmcrease and decrease of f d Give the values of X at which f has an absolute minimum or an absolute maximum e Give the intervals where the graph off is concave up f Give the intervals where the graph offis concave down g Give the values of X where the graph of f has in ection h Plot f 9 Graph a functionfwhich has a cusp at X 1 a vertical tangent line at X 2 a horizontal asymptote of3 and vertical asymptotes atX 2 and X 3 9 List the domain critical numbers intervals ofincrease intervals of decrease in ection points intervals of concave up and intervals of concave down for the function given Then graph the function and carefully label any local maXimums local minimums or points ofin ection fx 2x3 3xZ 12x 3 10 Given fx x2 2 xe 12 using P10 12 sketch the graph draw the rectangles and find Lf P and Uf P Also be able to work word problems from section 45 Skills review at end of chapter 4 58 59 602 64 65 76 Math 143 1 Exam 2 Review 1 Find the followinglimits ifthey exist a haw i e limx27l l z7gt0 5x 5 z7gto x 7 I v b ME f WW I Z7gt0 x If X7gt0 2x I m lt a i w i I c 7 g 11ml f z7gto x z7gto Lang 7 2 7 v 2 d nuxx 6 h rmw 0 H4 9 1 9 0 H0 6x 2 Determine ifthe following are continuous Ifthe function is not continuous state the type ofdiscontinuity x21 xlt1 3 fx 8 x1 Jump x3 xgtl 2x1 xlt2 b fx 8 x2 3 5 x3 xgt2 57x xlt72 C fx 7 x72 x175 xgt72 NOAJWP x1 ifxlt71 d foo 3c x2 ifxzil x1 ifx 3 3 Let foo k if x 3 Forwhat value of kwould fXbe continuous at X5 K L P Find A and B sothat X is continuous 6x171 xlt7l A f fx A x7l EL Bx3 xgt7l E 2 3 Given fx 1quot D find f393 ifit exists D39U x 73 x53 0 Find the derivative ofthe following fx32x714 My 2413103 Fr ysecz2x 539 a SeAZUbJ in 5W 5 I c fx3 410 ST g 1 L d fx 1006 le 5 A e fxL2x W 91x5quot 7 X f fxx2 2x x713 93903 Vi155 actStori ix ag9k h x m g fxw 39C KD 131 2 rx nsx h yx1x35x I I Hm 3 RJXH Sx 39glsmx 1 fxlicosx 410 Owingquot j fxsin 4x2 76xl I39lsz15n ly Axbwinstht 13 quot5 7 n y a jx 1y eotx k39 y 1 t1 39 T 1 l ft9sect97tan0 4515 5amp9 tame sec 6 7 Find 1 using implicit differentiation a x2y274x3y7 9 jljxq b sinxicosy720 11 Dj LDSXCJCj c xjixyy31 c m d f7 16 3 3 31quot on b 3353955 39yx xyi 3 dimlyMN e xy10 a a y t f xsin2y1 q L3 Tnasl g x23y235 In 33 I h cosxy4xy L 3 5mC u 43 Hy 5mep 8 Use differentials to approximate a 311801 8 41 399 b cos31quot 9 43 W3 9 Use the definition ofderivative to find the derivative of the following a fx3x2 7x2 Thrsh baaquot ka Mm 1 2 puke surc lieu use barred b fx notattun x5 c fxlxl d3 3 A 3 10 Fmdj 7x 72x x710 IVY ix 4 11 Findgat x72 for y4xllix3 56 2 37 12 Find the second derivative atthepoint 21 for x2 7 y2 3 393 13 Use interval notation to give the solution set to a x2xil3x4 so 00 U3 u 0 7 b x177x6gt0 wnuam i i 2 14 F1nd 26 5dx2x x may I 15 Aparticle is moving along the parabola yi 4X2 As itpasses 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 q L n 11 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 3 mm down the wall 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 Unl39tjscc 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 111500 radiansminute 39 39 7 At what rate 15 the shadow length decreasmg mm 19 Writethe equation ofthe tangent and normal line to a y2 7x60atthepoint 153 b 2x2 76xy y2 9 atthe point 151 a 71 5 3 7270 15 h 1153 0 N 3 3 quot0 quot 5 5 39ltx J 20 Find the critical numbers offand classify the extreme values given x e 31 fm 1quot of may I Us x 4 Lbs n139n391r hl 21 Find all local extreme and intervals of increas ing and drecreasing aor1 ml fx x3 76x2 MI 00 ind glam I a 3 dzcr 433 Elal local m C 446 22 Use the intermediate value theorem to show that the function fx 2x5 3xl has a root on the interval 712 Lani ll 3 F D quotI H13 7 LL047 has a fuel 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 gx 2 1 4 3 g39x 4 2 3 1 a M4 if hlfgl 17 h394 if hlfgl 6 h4 if hlgfl l 1 3 d 4 if hlgfl 8 h394 if ha f 0 if hlflgl 3 S foc L I5 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 a i E


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