Difference between revisions of "Math 22 Limits"
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which is read as "the '''limit''' of <math>f(x)</math> as <math>x</math> approaches <math>c</math> is <math>L</math> | which is read as "the '''limit''' of <math>f(x)</math> as <math>x</math> approaches <math>c</math> is <math>L</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> | 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> | ||
| + | |||
| + | ==Some Basic Limits== | ||
| + | For <math>b,c,n</math> are constant. | ||
| + | 1. <math>lim_{x\to c} b=b</math> | ||
| + | 2. <math>lim_{x\to c} x=c</math> | ||
| + | 3. <math>lim_{x\to c} x^n=c^n</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 20:28, 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)} as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} approaches Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c} is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L}
Note: Many times the limit of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)} as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} approaches Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c} is simply Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(c)} , so limit can be evaluate by direct substitution as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\to c} f(x)=f(c)}
Some Basic Limits
For Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b,c,n}
are constant.
1. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle lim_{x\to c} b=b}
2. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle lim_{x\to c} x=c}
3. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle lim_{x\to c} x^n=c^n}
This page is under constuction
This page were made by Tri Phan