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# Calculus & Analytic Geometry I MATH 131

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This 6 page Class Notes was uploaded by Dr. Cleo Wunsch on Thursday October 15, 2015. The Class Notes belongs to MATH 131 at New Mexico Institute of Mining and Technology taught by Josef Brown in Fall. Since its upload, it has received 8 views. For similar materials see /class/223626/math-131-new-mexico-institute-of-mining-and-technology in Mathematics (M) at New Mexico Institute of Mining and Technology.

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Date Created: 10/15/15

Final Exam Review Math 131 1 Find the domain of fx 9 x oo 3 and 0 3 2 Find cos arcsin x2 Vl x4 Build a right triangle so that X2 is the sin of one ofthe angles 3 Verify that f x x3 3x2 satis es the hypotheses of Rolle s Theorem on 0 3 Since the function is polynomial it is continuous and differentiable everywhere also f0 f3 4 Find the linear approximation to y J at a 4 5 If f x2x2x then fx x3x2C 6 Is fx lx ll differentiable for all x in 5 5 No at X l the slope is undefined Since the derivative is defined as a limit from the left we get 71 and from the right 1 The two do not agree so the derivative is not defined 7 If y 75 then d y 0 7239s is a constant dx 8 If f21f 27 and hxfx3 then h 2 h39ltxgt3fltxgt2f39ltxgth39lt2gt3f2gt2 f39lt2gt h 2312 7 21 4x l 2x3 9 If fx then nd f39l x 4y 1 gt2xy3x4y l gt3xl4y 2xy 2y3 3xl 4 2x 3xly4 2x gtyf391x 10 If fx 2x3 andgx x2 l then nd g of What is the domain of g of To be in the domai of the composition X must rst be in the domain of f Then fX must be in 3 2 the domain ofg We need 2x3 Z 0 gt x Z for the domain g of 42x3 l 2x3l given the domain restrictions already mentioned 11 Suppose that a particle travels along a straight line with vt t2 2 a Find the displacement of the particle for 0 S t S 4 4 341 2 2dt 2 th m 13333 0 0 b The total distance traveled by the particle for 0 S t S 4 J 4 t2 2dt I2 dt J t2 2dt J 0 524 J 4 2 t2dt t2 2dt d4403 8 Eml710 3 12 Determine the horizontal asymptotes and vertical asymptotes of y x x 3x3 2x1 xl3x2 3xl y 2x2 x3 x22 x HAy lim fx 3 VAx0x2 liiigfx c ligfltxgt c Find Q for the following dx a ysin2cos3x Chain rule y39 cos 2 cos3x2 sin 3x3 6 cos 2cos 3xsin 3x Implicit eyy39ex 6 yxy39 eyy39 e yxy39 ye y ex y39ey e yx yew ex 39 yew ex y ey e yx c yx2x Logarithmic lny2xlnx y39 2ln x 2 y lt gt y39 2lnx 2y 2lnx2x2 Evaluate the following I sinsx dx cos x 74 Ju395du TC C cos4 x ucosx du sinxdx 2x b Ie equot2dxJe 2e39 dxe 72 e 2xC 2 2 ux29 du2xdx 4 lJ x d x2 9 0 25 iju39lZalu u1255 32 29 15 Find lim L L HI lnx x l 1 1 1 n Hm 1imx xigt1im x HI lnx x l HI lnxx l HI 1nxx l x x l LH 1 1 11m gt11m HI xlnxx l H1llnxl 2 116 16 Find lgr Zx lx lgr Zx L In 1 2 1imM1nL xgt0 x 1im 21nL gte 2 L H0 l Zx 17 Sketch a possible graph of a function with the following properties Domain and Range First Derivative Second Derivative f00 f xgt00ltxlt11ltxlt2xgt2 fquotxgt01ltxlt2 f11 f xlt0xlt0 fquotxlt0xlt00ltxlt1xgt2 f30 f xoo jig H4 f39x oo 312 fltxgt 0 313 fltxgt O h VIL39r2hl gthir 2 i or z 7 dr Irr dh 2 dr lm 8Lmhr E 1000hr 2 250 21 A box with a square base and no top must have a volume of 32000 cm3 Find the dimensions of the box that minimize the amount of material used Verify with the second derivative test Ax24xy Vx2y320003y32w Ax2128000 x A392x w A3903x40 256 000 A 2 x3 x 403Aquot gt 039x 40 is aminimum

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