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# 113 Note for MATH 230 with Professor Simring at PSU

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This 7 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 17 views.

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Date Created: 02/06/15

10 Midterm Exam 1 Calculus 111 Sample A 10 points Show that the 4 points P1 0 0 0 P2 2 3 0 P3 1 711 P4 1 4 71 are coplanar they lie on the same plane and nd the equation of the plane that contains theml 10 points Find the equation of the plane that is equidistant from the points 321 and 737271 that is every point on the plane has the same distance from the two given points 6 points Find the vector projection of b onto a if a 4 20gt and b 111gtl p01nts ons1 er t e curve r cos 1 s1n J s1n l 1239C39dh t2tquottquottk a 8 points Find the unit tangent vector function Tt and the unit normal vector function Ntl b 4 points Compute the curvature Hi p01nts 1n t e engt o t e curve w1t parametrlc equatlon 10 39 F39 d h l h f h 39 h 39 39 rt e e sin t e cos tgt between the points 1 0 1 and e2 0 e2 p01nts spaces 1p 1s trave 1ng w1t acce eratlon 12 39 A h39 39 l39 39 h l 39 at e tsin 2tgtl At t 0 the spaceship was at the origin r0 000 and had initial velocity V0 100 Find the position of the spaceship at t TL 10 points Write the equation of the tangent line to the curve with parametric equation 1W lt 717t4gt7 at the point 11 1 12 points Using cylindrical coordinates nd the parametric equations of the curve that is the intersection of the cylinder 12 y2 4 and the cone 2 x 12 y2l This problem refers to the material not covered before midterm 1i 6 points Let fz y sinz2 y2 arcsiny2l Calculate 82 f Bray This problem refers to the material not covered before midterm 1i 12 points Show that the following limit does not exist 7z2yr 7 y 004 34 Justify your answer This problem refers to the material not covered before midterm 1 14040343 Mmmm Exam L Calculus UL Samplg s armsmm mxmjmmmmmwmwwamihu 2 armvmummmmmvemasawvem sz 1373 4E rmmmmmmmmm wmmvem spun m4 A77masmmammhmekmmvems 2m LLQ R2U unmasmwmmm 1 32 smut x nammmm a3 h amp 67mmmamwzpmmmmmmwmfmmmybms an and raw u 7 67mm mm Dummy hemmxmngmwnybms 21yxu m 42 a a mag Mann 0 mm mm mm mm 2 10 11 12 s Pomts Charge the pomt 272 N m zeatargulaz coozdmates to spheucal coozdmates Thu pmbzm mst t0 the mammal mt gamed heme mtdmm z s Pomts Charge the equation 7 7 z 1 m cylinducal coozdmates mto zeatargulaz cooxdh Hates Thu pmbzm mst t0 the mammal mt mwMEd heme mtdmm z 3 Pomts A pazucle moves thh position function W mam Fmd the Largenual component of accelezauon 3 Pomts Considex the cuzve rt Ssmti 4tj 3 costk The umt Largerquot vectoz Tz gooeti gj r gsmzk 1s gweh Fmd the cumtuze 13 8 Points Find the length of the curve rt 72 2t7 ln tgt from the point 17 2 0 to the point 62 261 14 8 Points Consider a particle Whose acceleration is given by at lttt2cos2tgt With initial velocity V0 lt1 07 1gti Find the velocity of the particle as a function of time Midterm Exam 1 Calculus III 10 Pornts Flnd an equatron ol the sphere that has center at 1 72 75 and passes through the orlgln Sample C 6 Pornts Flnd a vector m the opposrte drrectron as b 75 a 7 and has length 6 Let A 1111111 g 122 2 301 a 6 Pornts Flnd the area ol trrangle ABC b 6 Pornts Flnd the equatron ol the plane passrng through A B and c Wrrte the answer m the lorrn or by be g a 6 Pornts Flnd pararnetrrc equatrons ol the lrne whlch passes through the pornt 111 and rs perpendrcular to the plane 2r y e 0 b 6 Pornts Flnd the equatron ol the plane passrng through the pornt 111 and rs parallel to the plane 2r y e 0 a Pornts The rullrng lrnes on a cyllndel ol the cyllndel de ned by equatron y rs perpendrcular to check one wyplane yaplane warplane 5 Pornts Change the lollowrng cyllndncal equatron to a rectangular equatron and ldentlfy the surlace rifert 2rsrnb70 77m problem refers to 072 mterrd nut eobereb before rrebterrn 1 A Pornts The pornt 711 rsgwen m rectangular coordrnates Flnd the cyllndncal and spherrcal coordrnates lor thrs pornt 77m problem refers to 072 mbbenbb mt eobereb before mmtwm l A certarn surlace rs de ned by equatron 37 e2 a9 1 a A Pornts Flnd and sketch the traces on the horrzontal planes e 1 01 b A Pornts Whrch one ol the gures best rnatch wrth thrs equallons7 Crrcle the surlace III IV I II 10 11 10 Points Find symmetric equations of the tangent line to the curve given by the vector function rt t2 42 3 sint t4 a at the point P 001 Consider a curve 261 72W t 27ri z e sint7 y e cost7 a 2 Points Find the unit tangent vector Tti b 3 Points Find the principal unit normal Nti c 3 Points Find the binormal vector Bti d 2 Points Find the equation of the normal plane at t 0 e 2 Points Find the equation of the osculating plane at t 0i 8 Points A particle moves With position function W e2 n equot Find the tangential and the normal components of acceleration Midterm Exam I Calculus III Sample D l 10 Points Find an equation for the plane consisting of all points that are equidistant from P 71273 and Q 442 2 8 Points Find all values of I such that the vectors 1 73 zgt and 75 2 zgt are orthogonal 3 8 Points for each part For each of the following pairs of planes P1 P2 determine Whether P1 and P2 are parallel or intersectl If the planes are parallel explain and nd the distance between them if the planes intersect nd the line of intersection P1 z 2y 7 42 2 1 P2 72174y82l P1 z2y7422 2 P2 21 y 2 l 4 a 6 Points Sketch a graph of the surface 2 12 y 7 2 71 Find and label the points at Which the surface intersects the zaxis b 6 Points Find the equation of the curve of intersection C of the surface in part a and the plane y 72 5 Let C be the space curve traced by the vectorvalued function rt 4cos ti 4sin tj Stkl a 8 Points Find the equation of the line tangent to the C at the point 400l b 8 Points Find the curvature Ht at the point 74 0 3 c 8 Points Find the unit tangent vector Tt normal vector Nt and binormal vector Bt at the point 74037rl d 8 Points Find the length of the curve from 400 to 40 6 6 Let vt 4t 7 3 Set 4 cos 2t be the velocity vector of a particle at time t a 6 Points Find the acceleration vector atl b 6 Points Find the position vector rt if the particle has has initial position r0 012 7 10 Points A particle moves With position function rt t21t3t71gtl Find the tangential and normal components of acceleration at the point 2 l 2

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