The Limit of a Function - Revision history

Khanh: /* Resources */

2022-01-15T21:41:15Z

Resources

2021-10-28T23:31:56Z

Resources

2021-10-27T20:23:23Z

Resources

2021-10-27T20:22:00Z

Resources

2021-10-18T19:09:46Z

Resources

2021-10-18T19:08:24Z

2021-09-29T00:09:29Z

Definition: (Formal definition of a limit)

2021-09-28T19:41:25Z

Formal Definition of a Limit Being Infinity

2021-09-28T18:58:40Z

2020-08-25T18:45:41Z

minor edit

← Older revision		Revision as of 21:41, 15 January 2022
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	* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionWS2.pdf The Limit of a Function Worksheet 2]		* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionWS2.pdf The Limit of a Function Worksheet 2]
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	* [https://youtu.be/HYSI-AHUqRM What is a Limit? Basic Idea of Limits] by patrickJMT		* [https://youtu.be/HYSI-AHUqRM What is a Limit? Basic Idea of Limits] by patrickJMT

← Older revision		Revision as of 23:31, 28 October 2021
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−	* [https://youtu.be/QfPqRMqP5kU Calculus 1 - Introduction to Limits] by The Organic Chemistry Tutor

	* [https://youtu.be/HYSI-AHUqRM What is a Limit? Basic Idea of Limits] by patrickJMT		* [https://youtu.be/HYSI-AHUqRM What is a Limit? Basic Idea of Limits] by patrickJMT

← Older revision		Revision as of 20:23, 27 October 2021
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	* [https://youtu.be/kG_p2vKApOE Lots of Limit Examples, Part 1] by patrickJMT		* [https://youtu.be/kG_p2vKApOE Lots of Limit Examples, Part 1] by patrickJMT
		+
		+	==Licensing==
		+	Content obtained and/or adapted from:
		+	* [https://en.wikibooks.org/wiki/Calculus/Integration_techniques/Infinite_Sums Infinite Sums, Wikibooks: Calculus/Integration techniques] under a CC BY-SA license
		+	* [https://en.wikibooks.org/wiki/Calculus/Formal_Definition_of_the_Limit Formal Definition of the Limit, Wikibooks: Calculus] under a CC BY-SA license

← Older revision		Revision as of 20:22, 27 October 2021
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	* [https://en.wikibooks.org/wiki/Calculus/Integration_techniques/Infinite_Sums Infinite Sums], Wikibooks: Calculus/Integration techniques		* [https://en.wikibooks.org/wiki/Calculus/Integration_techniques/Infinite_Sums Infinite Sums], Wikibooks: Calculus/Integration techniques
		+
		+	* [https://en.wikibooks.org/wiki/Calculus/Formal_Definition_of_the_Limit Formal Definition of the Limit], Wikibooks: Calculus

	* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionPwPt.pptx The Limit of a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.		* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionPwPt.pptx The Limit of a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

← Older revision		Revision as of 19:09, 18 October 2021
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	==Resources==		==Resources==
		+
		+	* [https://en.wikibooks.org/wiki/Calculus/Integration_techniques/Infinite_Sums Infinite Sums], Wikibooks: Calculus/Integration techniques

	* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionPwPt.pptx The Limit of a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.		* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionPwPt.pptx The Limit of a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

@@ Line 139: / Line 139: @@
 :<math>\lim_{x\to c}f(x)=-\infty</math>
 or
-:<math>f(x)\to-\infty</math> as <math>x\to c</math> .
+:<math>f(x)\to-\infty</math> as <math>x\to c</math>.
 ==Resources==

@@ Line 5: / Line 5: @@
 The intuitive definition of a limit is inadequate to prove anything rigorously about it. The problem lies in the vague term "arbitrarily close". We discussed earlier that the meaning of this term is that the closer <math>x</math> gets to the specified value, the closer the function must get to the limit, so that however close we want the function to the limit, we can accomplish this by making <math>x</math> sufficiently close to our value. We can express this requirement technically as follows:
-==Definition: (Formal definition of a limit)==
+==Formal definition of a limit==
 Let <math>f(x)</math> be a function defined on an open interval <math>D</math> that contains <math>c</math> , except possibly at <math>x=c</math> . Let <math>L</math> be a number. Then we say that
 :<math>\lim_{x\to c}f(x)=L</math>

@@ Line 119: / Line 119: @@
 ==Formal Definition of a Limit Being Infinity==
-Definition: (Formal definition of a limit being infinity)
+Let <math>f(x)</math> be a function defined on an open interval <math>D</math> that contains <math>c</math> , except possibly at <math>x=c</math> . Then we say that
 :<math>\lim_{x\to c}f(x)=\infty</math>
 if, for every <math>\varepsilon</math> , there exists a <math>\delta>0</math> such that for all <math>x\in D</math> with
@@ Line 126: / Line 125: @@
 we have
 :<math>f(x)>\varepsilon</math> .
 When this holds we write
 :<math>\lim_{x\to c}f(x)=\infty</math>

@@ Line 3: / Line 3: @@
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionPwPt.pptx The Limit of a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.
-* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214-2.2TheLimitOfAFunctionNotes1.pdf The Limit of a Function] notes created by Instructor Beatty,UTSA.
+* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214-2.2TheLimitOfAFunctionNotes1.pdf The Limit of a Function] notes created by Instructor Beatty, UTSA.
-* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionNotes.pdf The Left and Right Hand Limit] notes created by Instructor Beatty,UTSA.
+* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionNotes.pdf The Left and Right Hand Limit] notes created by Instructor Beatty, UTSA.
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214-2.2TheLimitOfAFunctionWS1.pdf The Limit of a Function Worksheet 1]