midterm2-b

midterm2-b - Name: PID: Sec. No: Sec. Time: TA: Math 10C...

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Name: PID: TA: Math 10C (Klep) Midterm Exam 2 February 27,2OO8 Sec. No: Sec. Time: Turn off and put away Aour cell phone. You may use one page of notes, but no calculators, books or other assi,stance. Read each quest'ion carefullg, and answer each questi,on completely. Show all of your work; no credi,t wi,ll be gi,aen for unsupported, answers. Write gour solut'ions clearly and legi,bly; no cred'it wi,ll be gi,uen fpr illegible soluti,ons. If any quest'ion i,s not clear, ask clarificati,on. -4 TT Points Score I 8 ,. 10 3 4 T2 40
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1. Let d.: (6,L, -2) and d : Zi - ZE. (a) (f pts) Find a vector orthogonal to both il, and d. uLu{ = \;t 1\ lg t2 -a I -- -r.l G i- 3il * | )j\= - ?f *ui 4Q (b) (3 pts) What are two unit vectors orthogonal to both 17 and d ? ll.,uxltl a .JQ-l6a.a1 *? qq.f ***3* a\ go 4t4 -n/nL '*/-J .t7 t& t{ rr r Vlt a. -3 **f Y l-tF" j /\ 7/n \& 'T
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2. Consider the function z : f (r,A) er-a. (u) (5 pts) Plot the vertical cross-sections when y is fixed to -1,0 and 1. ., +\ "t u*u /-\ a ;,''' -?**l (b) (5 pts) Write down the equations for the contours at heights 1, e, and e2, and draw a contour diagram with these three contours clearly labeled. I --- gx*? t = Tx-"t €-'" , tx'Y rGF O = Y'? rG? l: X-'tf iFF 3" X*u}
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midterm2-b - Name: PID: Sec. No: Sec. Time: TA: Math 10C...

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