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# Class Note for MATH 1431 at UH

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This 9 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 19 views.

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Date Created: 02/06/15

Let 279 Use the graph of f to nd 0073 af3 3 lim 1 C 11m 1 d1imfw zHB z 3 1H3 Use the graph of f to nd af5 3 lim 1 C 11m 1 d1imfw zHS z 5 1H5 Example Use the graph of f to nd af2 3 lim x C lim x d1im x 1H72 3H72 aHiZ ef4 1 lim 1 g lim 1 h1imfw anall z 4 1H4 Example lim m 3H0 z Let Use the graph of f to nd af0 3 lim 1 C 11m 1 d1imfw zHO z 0 1H0 Example Use the graph of f to nd af3 b 1111 x C 11m x d 11m x magi 1H3 ef7 1 lim 1 g lim 1 h1imfw z 7 z 7 1H7 Example lim 1H2 z 7 2 LS 1v 1m 1990 2 2mm 2m 21 M 72 40 rwo 4000 moo mu H Let Use the graph of f to nd a fa b 1111 x 0 11m x d 11m x may 1H2 Example 7 2 Let 96 i Use the graph of f to nd 171 af1 3 lim 1 C 11m 1 d1imfw z l 3H1 1H1 7V Example hm smi man m 3 5mm Let sin Use the graph of f to nd 2 ND b 111 x 0 11m x d 11m x 1 04 1H0 Example L 95 7 x mmnal Use the graph of f to nd x irrational we b gigm c zlirgfm d gm 13 Theorem An Important Theorem Theorem 1 mmd and only both lim L and lim L z c an c 2 Section 22 De nition of Limit 21 De nition of Limit De nition of Limit 5 6 statement We say that 1 1 r A 1 C x 1 w I I I 1 rm each s gt0 theve ems n a man that lim L 307m if mm Am 1 1 1 then rL HQ 1 22 Examples Example lim2x 7 1 3 Show that 111295 7 1 3 I 2 3 2 25 im2x 13 r7gt 2 Let 5 gt 0 We choose 6 5 such that if 0lt1z721lt6 then 21 7 1 7 31lt5 Example lim 2 7 3x 5 Show that T171132 7 3x 5 fx 2 3x x Hm 2 73X 5 x 39gl Let 5 gt 0 We choose 6 5 such that if Olt xi71 lt6 then 273x75 lt5 23 Three Basic Limits 1111 x c Sh w that lim 1 c was 4 f x x o 1 m q L Let 5 gt 0 We choose 6 5 such that if0lt acic lt67 then xic lt5 lim H Sh w that im was imxc X gtc Let5gt 0 We choose 5 such that if Olt acic lt67 then Hz i cHlt5 lim k k S w that 1111 k k was k e I I I I I I I I I I L75 c 05 3 Hmkk 39gtc Let 5 gt 0 We can choose any number 6 gt 0 such that if0lt acic lt67 then kik lt5 Lecture 1Section 21 The Ideal of Limit Section 22 De nition of Limit Jiwen He 1 Section 21 The Ideal of Limit 11 The Ideal 0f Limit Graphical Introduction to Limit o In taking the limit of a function f as x approaches c7 it does not matter Whether f is de ned at c and7 if so7 how it is de ned there 0 The only thing that matters is the Values that f takes on When x is near c 12 Examples 2 7 9 Example lim x was x 7 3

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