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Math210-first-fall2019

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School
University of Illinois, Chicago**We aren't endorsed by this school
Course
MATH 210
Subject
Mathematics
Date
Jan 14, 2025
Pages
10
Uploaded by MateApePerson1066
Math210 first fall2019Calculus Iii (University of Illinois at Chicago)Scan to open on StudocuStudocu is not sponsored or endorsed by any college or universityMath210 first fall2019Calculus Iii (University of Illinois at Chicago)Scan to open on StudocuStudocu is not sponsored or endorsed by any college or universityDownloaded by Ali Hamzah (alihamzah06102024@gmail.com)lOMoARcPSD|43629157
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DO NOT WRITE ABOVE THIS LINE!!MATH 210 Exam 1October 03, 2019Directions. Fillineachofthelinesbelow. Thenreadthedirectionsthatfollowbeforebeginningtheexam.YOU MAY NOT OPEN THE EXAM UNTIL TOLD TO DO SO BY YOUR INSTRUCTOR.•All of your work must fit within the boxes. Nothing outside of the box will be graded!Name (print)netidUIN•A solution for one problem may not go on another page.•Show all your work. Unjustified answers are not correct. Make clear what your final answer is.•Have your student ID ready to be checked when submitting your exam.Check next to your instructor’s name (and lecture time, if applicable):Abramov 11AMSparber 2PMEinstein 1PMSparber 1PMKobotis 8AMLear 10AMHamdan 4PMDai 11AMPourarian 1PMGreenblatt 12PMKashcheyeva 3PMChow 10AMPourarian 3PMEinstein 2PMWhyte 12PMShulman 9AMLear 9AMSwitala 2PMMichelen 2PMDatta 1PMHamdan 5PMChu 11AMSwitala 9AMProtsak 10AMDatta 2PMDownloaded by Ali Hamzah (alihamzah06102024@gmail.com)lOMoARcPSD|43629157
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Write solution only inside the box1.(15pt)Letu=(1,3,−2)andv=(1,1,−1).(a) Find the projection ofuontovand call this vectorw.(b) Find the vectoru−w.(c) Show thatu−wis orthogonal tov.Downloaded by Ali Hamzah (alihamzah06102024@gmail.com)lOMoARcPSD|43629157
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Name:UIN:Write solution only inside the box2.(10pt)Find the area of the triangle with vertices (2,1,1), (3,1,−1) and (2,1,3).Downloaded by Ali Hamzah (alihamzah06102024@gmail.com)lOMoARcPSD|43629157
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Write solution only inside the box3.(15pt)Consider the line going through the points (1,2,−1) and (3,2,1).(a) Find a vector equation for this line.(b) Determine whether the point (2,2,0) belongs to this line or not.Downloaded by Ali Hamzah (alihamzah06102024@gmail.com)lOMoARcPSD|43629157
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Name:UIN:Write solution only inside the box4.(10 pt)Find the equation of the plane that contains the point (1,2,−3) and is perpendicular to theline with vector equationr(t)=(2−3t,3+t,−1).Downloaded by Ali Hamzah (alihamzah06102024@gmail.com)lOMoARcPSD|43629157
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Write solution only inside the box5.(15 pt)We consider a motion for which:•its velocity is given byv(t)=(−2cost,2sint,0).•the position vector of the corresponding object fort=0 isr(0)=(−1,1,1).Find the vector equation of the positionr(t) of the above motion.Downloaded by Ali Hamzah (alihamzah06102024@gmail.com)lOMoARcPSD|43629157
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Name:UIN:Write solution only inside the box6.(10 pt)Find the length of the trajectory ofr(t)=(bigglnt,t22,√2·t)biggfromt=1 tot=2.Downloaded by Ali Hamzah (alihamzah06102024@gmail.com)lOMoARcPSD|43629157
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Write solution only inside the box7.(10 pt)Use the two path method in order to show that iff(x,y)=xy2x2+y4, then the limitlim(x,y)→(0,0)f(x,y)does not exist.Downloaded by Ali Hamzah (alihamzah06102024@gmail.com)lOMoARcPSD|43629157
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Name:UIN:Write solution only inside the box8.(15 pt)Letf(x,y)=xx+3y. Computefx(−2,1) andfy(−2,1).Downloaded by Ali Hamzah (alihamzah06102024@gmail.com)lOMoARcPSD|43629157
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