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quiz2 solutions nikki armstrong

quiz2 solutions nikki armstrong - Quiz/7 NC/3 Total/10 Math...

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Unformatted text preview: Quiz /7 NC /3 Total /10 Math 1A - Quiz 2 - Febmzry 8, 2008 NAME 1, Show that there is a root of the equation in the given interval. 2x3+x2+2=0, (— 2, — 1) Letf(x)=2x3+xz+2 thenf(— 2)=— 10<0 and f(~1)=l>0 So, since f (x) is a cantirzuousfimction, then by I VT there is a mat in the interval (— 2, — 1) because f (— 2) <0 and f (~ 1) >0 2. Prove that lim 1 ‘ ""”(x+3) =00 We need to show that for every M>0 there is a 5>0 such that 1 4 >M (x + 3) So we manipulate the right to make it look like the Iefi . . . which will tell us what 8 needs to be‘ (Remember, it is aurjob here topick 8) l 1 l I >M—>—>x+3 —3 ‘>x+3 (M). M < ) 2 I I So this tells us we should pick 8 = ~1—1 M? 1 1 “’ A >M M7 (x + 3) |x+3i<5 implies So, then VM>0 |x+3|< 3. Use the definition ofthe dexivutive to find f ’ (a) for f (x) = 3 — 2x + 4x2 (3—Zx+4xz)-(3—2a+4a2) zen—Fa x a x_a _ —2x+2a+4x1—~4a1_. —2(x'a)+4(Xz-a‘) _’H“ x—a —H‘ x—a =xfiq—2+4(x+a)=—2+4a+a)=—2+8a NOTECARD BONUS QUESTION: (1 point) Find the limit: . 4—v vl-Elhl't‘t—V' ...
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