# metu-mat119.e166421.set2 - Sena Aksoy MAT 119 5 Fall 2010...

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Sena AksoyMAT 119 5 Fall 2010WeBWorKassignmentset2isdue:10/20/2010at06:00am EEST.(This is early Sunday morning, so it needs to be done Satur-day night!) Remember to get this done early!This assignment covers sections 8.1, 8.2, 8.3, 8.4, 8.5, 8.7,8.8, and 9.1, 9.2.1.(1 pt) Determine the infinite limit of the following func-tions. Enter INF forand MINF for-.1. limx52(x-5)62.limx3+2x-33.limx5-2(x-5)34. limx01x2(x+7)
INF(correct)Note: Enter ’DNE’ if the limit does not exist or is not defined.a) limx→-1-F(x)=b) limx→-1+F(x)=c) limx→-1F(x)=d)F(-1)=e) limx1-F(x)=f) limx1+F(x)=g) limx1F(x)=h) limx3F(x)=i)F(3)=
2.(1 pt) Consider the following limitlimx8104-8x-|x2-13x||x2-169|-105
3.(1 pt) Let F be the function below.If you are having a hard time seeing the picture clearly, clickon the picture. It will expand to a larger picture on its own pageso that you can inspect it more clearly.Evaluate each of the following expressions.Note: Enter ’DNE’ if the limit does not exist or is not defined.a) limx→-1-F(x)=b) limx→-1+F(x)=c) limx→-1F(x)=d)F(-1)=e) limx1-F(x)=f) limx1+F(x)=g) limx1F(x)=h) limx3F(x)=i)F(3)=
1
4.(1 pt) Consider the functionf(x) =5x-cos(x)+4 on theinterval 0x1. The Intermediate Value Theorem guaranteesthat there is a valuecsuch thatf(c) =kfor which values ofcandk? Fill in the following mathematical statements, giving aninterval with non-zero length in each case.For everykink,there is acincsuch thatf(c) =k.SOLUTIONWe knowfis continuous, and thatf(0) =3 andf(1) =9-cos(1). Thus, we know by the Intermediate Value Theoremthat for anykbetween these values there must be acbetween 0and 1 for whichf(c) =k. (Of course, we could also pick anyother range of valuesc0xc1, noting that the IntermediateValue Theorem guarantees that there is acin that range suchthatf(c) =kfor anykinf(c0)kf(c1).)
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