Anti derivatives a 6x 8x axdx x 3 Math Discussion 7 2 24 Revision Derivatives a f x bx3 x 4 1 f x 18x2 b f x sim ix f x 2 cos 2x c f x 2x3 tan y f x 6x2 tan x 2x3 seax Increasing decreasing R x x 1 x 2 stationary points R x 0 R X x 2 z x z x 1 R X 0 When x 2 and X 0 D Increasing 0 0 V 2 8 Decreasing 0 2 Math 132 Lecture 8 2 24 a P 0 3000 rate of growth 10007t what Ihour a N t number of bacteria is p t after N 0 3000 d07t bacteriale N 1 N 0 J d7Netcana N 1 N O JdN 3000 1000 I O 3000 1000 zt It 3000 1000 6083 6083 5 5 Substitution Ex 94x3 3 xi 7 by A 4 u S xY Sut Ludx f 4 u7 f u a u stx ing u 5 x4 t Je f u f Sau dx flu Ex Procedural Sux s x4d u S xt 4 Sa as Su7 du Ex Sos Osino to bu d coso w u cosO Ex de 4 Sis iSi tan u c Itan xY C de sino sin Su So x a I d 49 4x 4 uX n 49 1 49 x 4 Mu dy T Ex u h x Sen du S S do Note t n ut it Su du u 49 2 u Eu a8u c 2 4354x3 98 49 4x T7 C u 497X definiteDate b F a Ex Sd Ex ea u e 2z A t du 1 In 1e 2z c e 22 0 20 Mn e 22 1 55 3 HW Ex g x fHide fit MFF from t 0 to t x 127 Ju 6 4 dx 2 215 2 25 4 b w 8 2 6 25 7 d 8 Ext f set 10 a jv 3 mu 13 7 lu2 28 1 6 luz 7 36 36 45 Ste dx Set de 36 5x M Se bite du S dx dx Au S de 369 unde du due t y Sin 4 3 d du sofin t Sna 6 7 geMint31 Jin 3 d In 4 30sx ws In 4 3sinf sinx In 4 3csX cosX In 4 3 sinx da 8 Jaco SS so Sz Stan o 70 C I T 3 zx Ex3 d 2 Star 0 70 11 2x 2 S dx b 3 S4x2 6 dx u bxg garcana 6 2x a 4x2 3 dx 2x3 6x 36x2 27 2 r 2x 12x 3x2 27x 10 2 2 12 23 32 27 2 32 96 12 54 106 2 2 2 2 150 44 2 7 Fe Osin get Scosx1 9e 8 9 8 9 vCt t It S 2t sc se E 8 m 9 3333 36 10 t 0 P 0 6000 6 1 breas between cars Chapter Exiy f x y g x Approximate rectangle width X Area f x g x Xg f x brea between I curves g x d where f x g x a Sketch the region enclosed byces ye Yes x2zx 11 3 15x thifdx Find IIIIIe2 o Fitzud 3 6 Sketch the region enclosed by y z y 8x y Fat perm lower curve y x upper cre Se lower wive 1 ys 2 y z 8x 2 i y X not as 16 x2 x 4 rot yas x 0 4 Fox Ec O My ben 64 1 your function is not based on x Ex when X yz doesNotparstherehere not a function of x however instead of subtracting from top to bottom its rightto left d ff gly dy d C g y f y 1 3 1 dx fy u du 4 HW5 5 i 3 x4 A u coso An since du sind do u En x du d u x2 6x M 2 x 6 2 x 3 MX x dy 2 Jus o sino do d 3 3 3 Md Su 3 3 4 x 3 dx d du 5 I dx Jud U In data du X 6 Sdxudu U Ear 7x a 7 S 8 S em u X S x c da 3 d 48 256 10 Jedz d Melt 13 12 tand see o do u 25 3z du du e 31z U 2 tar O dy seco do du secod Slus d joj out at 2 S du u 3 x2 du 2 4 12 dx d u 2 2x 16 4x4xyx4x4x4 d 10x du de 6 60 26 32536 49 196 316 16 16 X 16 2560 To96 Math 132 Discussion Fundamental Theor of Calculus PI F x SEd F x f x Pati If xdx F b Fla F x f a Ex1 find f x 2 u 1 Stand 1 tan tdt t feta e F O O O f x tant 2x 2 E2 f x 1 dx 2 x 7 25 Indefinite integrals Sattanodo Sa seco do seco Of tan O C tap0 1 seco as and sinto coso 1 Calculate displacement d v t t t distance traveled s S t CH OXt 2 t soSridt dt j slo S vo Chapter 6 2 Volumes of Revolutions Cylinder Rightsinder conquent circle bases in alignment Right willer upinder Circular Cylinder B although the bares are not 6 are still congruent in alignment they Right elliptical cylinder Volume of rightlinder Area of base height u distance between bases Volume of right circular cylinder Rh Right Parallel cylinder 11 B Volume of annular right circle cylinder V Rh arh V R rz h 6 Find the volume of a solid of rotating the area under y and X axis betweenX 0 X 1 about the X axis revolution obtained by Y in order to get the answer you mustT find the Noume by rotating the graph 360 Ov and find the volume of y Riemann Sum Elemental disk volume Area ofdisk at value of lik x X Radius of disk at height of rectangle xy at x enclosed by 6 Region R is rotated about the X axis Find the volume of the generated soli y x y 2x my 2 2x x2 2x th6 HW 1 S1hx 2x d 4x x x 4 x O x x3 x2 2x2 2 2 3 32 32 32 2 Six y y2 y2 by dy juy joytydyfights e e 18 6 y y dy S y 8dy 5 2 yz 7 i 4 yz y y y 12 z y 3 1 7 3 12 I 63 32 Y 44 mos y m4 m os 4th 2 um 8 8 gout lysoas a Sty y g y 4 y 2 Sy 9 218 2 dy loy 16 32 3 4 z zagkx dx ze 7 we d 10 gioe Sos gis 7d M sin x x 53 7x 14ein s HW et y 2 y In 3x 4 gly dy ey 3x x e a 5 A x sir v Y x n x x x …
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