Limit Quiz Review Answers Let ( ) f x be the function whose graph is ...
Limit Quiz Review Answers Let ( ) f x be the function whose graph is ...
Limit Quiz Review Answers Let ( ) f x be the function whose graph is ...
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<strong>Limit</strong> <strong>Quiz</strong> <strong>Review</strong> <strong>Answers</strong><strong>Let</strong> f x <strong>be</strong> <strong>the</strong> <strong>function</strong> <strong>whose</strong> <strong>graph</strong> <strong>is</strong> shown.y<strong>Let</strong>g x<strong>be</strong> <strong>the</strong> <strong>function</strong> <strong>whose</strong> <strong>graph</strong> <strong>is</strong> shown.Use th<strong>is</strong> <strong>function</strong> and f at left to evaluate <strong>the</strong>following limits. If <strong>the</strong> limit does not ex<strong>is</strong>t, explain.y22-4 -2 2 4x-4 -2 2 4x-2-2Evaluate each limit or explain why <strong>the</strong> limit doesn’tex<strong>is</strong>t.1. f xlim 2x02. f xlim 1x33. lim f xx 1 DNE—different limit from eachsidelim f x 14. x25. f xlim 1x26. f xlim 1x27. f xlim 0x28. f xlim 0x19. lim f xx 4 DNE---not in domain10. f xlim 2x411. lim 12.f x g xx 1 x DNE—limits differentfrom each side f lim x1g x DNE---same as 1113. f xg xlim 0x314. g f xx2lim115. lim f x g xx1Evaluate <strong>the</strong> limit ifx1 x1DNE---same as 11xlim f 5 andlim g x 2 . If <strong>the</strong> limit does not ex<strong>is</strong>t, explainwhy.16. f x g xlim 5 2 3x117. f xg x18.lim 10x1f x limx1g x2DNE (infinite) since non-zerodivided b y zero.
19. Explain why you cannot evaluate lim f g xBecause we don’t knowLook back at <strong>the</strong> <strong>function</strong>ff 2 <strong>be</strong>ginning of th<strong>is</strong> practice sheet.x1x <strong>graph</strong>ed at <strong>the</strong>20. State <strong>the</strong> 3 part definition of continuity.f a ex<strong>is</strong>ts* * lim f xxaex<strong>is</strong>ts* lim f x f ax a21. State <strong>the</strong> location of a d<strong>is</strong>continuity on <strong>the</strong><strong>graph</strong> and explain which part of <strong>the</strong> continuitydefinition fails.At x = 2, <strong>the</strong> third condition above fails.22. State <strong>the</strong> location of ano<strong>the</strong>r d<strong>is</strong>continuity thatviolates a different part of <strong>the</strong> definition ofcontinuity and explain your reasoning.At x = -1, <strong>the</strong> 2 nd part of <strong>the</strong> definition fails.Evaluate each of <strong>the</strong> following limits if possible. If<strong>the</strong> limit does not ex<strong>is</strong>t, say so.23.x22lim 2x5 324.lim x 1x1DNE: Does not have a left side25.xlimx323x10x 3 since <strong>is</strong> nonzero/zero26.2x 3xlim 3x3x 3
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