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C1.2 Lecture Notes

by: Kayla Notetaker

C1.2 Lecture Notes STAT 1102 - 003

Kayla Notetaker
GPA 3.11
Ron Kershner

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Comprehensive notes and explanations of all lecture notes taken in class for C1.1. This is Ron Kershner's class for Quantitative Methods for Business II.
Ron Kershner
Class Notes
Quantitative Methods for Business II, Business II, stat, 1102, Stat 1102, quantitative, methods, for, business, II, 2, business 2, Quantitative Methods, methods for business, temple, University, Temple University, Ron, Ron Kershner, chapter two, Lecture
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This 3 page Class Notes was uploaded by Kayla Notetaker on Saturday September 26, 2015. The Class Notes belongs to STAT 1102 - 003 at Temple University taught by Ron Kershner in Fall 2015. Since its upload, it has received 44 views. For similar materials see QUANTITATIVE METHODS FOR BUSINESS II in Statistics at Temple University.

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Date Created: 09/26/15
C12 Algebraic Limits Continuity quotPlugIn rule Theorom for any rational function with a in the domain of F Iim xaFx Fa Meaning We can find the limit as x approaches a by evaluating fx at x a Properties of Limits 1 The limit of a constant constant a LimCC 2 Limit of a function to a power limit of the function to that power a Limfx quotn limfxquotn 3 Limit of a sumdifference sumdifference of the limits a Limfx gx Iimfx 4 Limit of product product of limits 5 Limits of quotients quotient of limits 6 Limit of constant times a function constant times the limit The properties are not used to evaluate Limits Finding Limits Algrebraically 2 steps 1 Plug the limit into the function 2 If the limit is not defined in step one then simplify by factoring the function and plug the limit in again a If the limit is STILL undefined then the limit does not exist Example Limx 13X 2 1 Plug in the limit 1 into the function a 31 2 2 Simplify a 3 2 b 5 c The limit is 5 as x approaches 1 lim x 1 3x5 4x4 3x 6 1 Plug in 1 a 315 414 31 6 b 343610 c The limit as x approaches 1 is 10 lim H 2 3x2x 14 x2 4 1 Plug in 2 2 3222 1422 4 3 342 144 4 4 00 5 Here the limit is undefined at x 2 so now we go to step two factor the function and plug in two again 6 3x 7x 2 x 2x 2 7 The x 2 cancel leaving 3x 7x 2 8 Plug in 2 9 32 72 2 1o 6 72 2 134 11 The limit as x approaches 2 is 134 Definition of a Continuous Function 1 If fa exists 2 The limit of fa exists 3 If the limit of fa fa A function is continuous over an interval if it is continuous at each point in that interval Example Is the function Fx 13 x 4 x lt 3 2x 1 x 2 3 Iim x 3 13 x 4 the limit as x approaches three from the left 13 3 4 5 Iim x 3 13 x 4 the limit as x approaches three from the right 13 3 4 5 These limits match so the limit exists BUT is the function continuous To find out if it is continuous evaluate the function at x 3 13 3 4 5 The limits as x approaches 3 5 and the function at x 3 is 5 therefore the function is continuous


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