Difference between revisions of "Math 22 Limits"
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Note: Many times the limit of <math>f(x)</math> as <math>x</math> approaches <math>c</math> is simply <math>f(c)</math>, so limit can be evaluate by '''direct substitution''' as <math>\lim_{x\to c} f(x)=f(c)</math> | Note: Many times the limit of <math>f(x)</math> as <math>x</math> approaches <math>c</math> is simply <math>f(c)</math>, so limit can be evaluate by '''direct substitution''' as <math>\lim_{x\to c} f(x)=f(c)</math> | ||
| − | == | + | ==Properties of Limits== |
| − | + | Let <math>b</math> and <math>c</math> be real numbers, let <math>n</math> be a positive integer, and let <math>f</math> and <math>g</math> be functions with the following limits | |
| − | + | <math>\lim_{x\to c} f(x)=L</math> and <math>\lim_{x\to c} g(x)=K</math>. | |
| − | + | Then | |
| − | + | 1. Scalar multiple: <math>\lim_{x\to c} [bf(x)]=bL</math> | |
| − | + | ||
| − | |||
This page is under constuction | This page is under constuction | ||
'''This page were made by [[Contributors|Tri Phan]]''' | '''This page were made by [[Contributors|Tri Phan]]''' | ||
Revision as of 19:31, 13 July 2020
The Limit of a Function
Definition of the Limit of a Function If becomes arbitrarily close to a single number as approaches from either side, then which is read as "the limit of as approaches is
Note: Many times the limit of as approaches is simply , so limit can be evaluate by direct substitution as
Properties of Limits
Let and be real numbers, let be a positive integer, and let and be functions with the following limits and . Then 1. Scalar multiple:
![{\displaystyle \lim _{x\to c}[bf(x)]=bL}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f3002341fe6d51854940848132f27c2f644d1828)
This page is under constuction
This page were made by Tri Phan