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Lecture 4 Notes - Continuing Limits

by: nichl

Lecture 4 Notes - Continuing Limits 01:160:161

Marketplace > Rutgers University > Chemistry > 01:160:161 > Lecture 4 Notes Continuing Limits

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Limits, Squeeze Theorem
General Chemistry I
Class Notes
Math, Calculus, Limits, Squeeze Theorem
25 ?




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This 2 page Class Notes was uploaded by nichl on Friday September 16, 2016. The Class Notes belongs to 01:160:161 at Rutgers University taught by in Fall 2016. Since its upload, it has received 9 views. For similar materials see General Chemistry I in Chemistry at Rutgers University.

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Date Created: 09/16/16
Calculus I Lecture 4 9/16/16 Limits tell you what may be going on at a point by looking at what is going on around it Squeeze Rule ???? ???? ≤ ???? ???? ≤ ℎ(????) on an open interval containing c ???? ???? is known,ℎ ???? is known,???? ???? is unknown but part of inequality above lim????(????) = ???? andlimℎ ???? = ???? then lim????(????) = ???? ????→???? ????→???? ????→???? Example 1 ???? ???? = ????sin , − ≤ ???? ≤ 1 ???? ???? ???? ???? ???? = ????| | ℎ ???? = −|????| Because: lim ℎ ???? = 0 and lim ???? ???? = 0 ????→0 ????→???? Then: lim ???? ???? = 0 by definition above ????→0 Calculus I Lecture 4 9/16/16 Rules of Limits: mit_laws.html Example 2 lim cos????−1 Multiply by conjugate ????→0 ????2 cos????−1 (cos????+1) cos ????−1 sin ???? lim ????2 ∗(cos????+1)= lim ???? (cos????+1)= ???? (cos????+1) ????→0 ????→0 2 lim sin ????= 1 Multiply by (according to rules above) lim 1 = 2 ????→0 ????2 ????→0 cos????+1 1 = 2 Practice 1 2 lim ???? +3????−10 = 8 By direct substitution ????→0 3???? +5????−7 35 Practice 2 1+tan???? ???? 1 li???? csc????+1 Substitute in4with the knowledge that csc???? = sin???? ????→ 4 1+tan???? 1+1 2 li???? csc????+1 = 2+1 = 2+1 ????→ 4 √ √ Practice 3 ???? −4????−4 lim Cannot factor, look graphically or plug in values close to 2 ????→2 ???? −????−2 Discover that denominator gets really small as numerator approaches -8 2 Therefore, lim???? −4????−4 = −∞ DNE ????→2 ???? −????−2


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