Math 210, Week 1 - Intro to Limits
Math 210, Week 1 - Intro to Limits Math 210
University of Louisiana at Lafayette
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This 2 page Class Notes was uploaded by Cynthia Ndulaka on Friday July 15, 2016. The Class Notes belongs to Math 210 at University of Louisiana at Lafayette taught by Professor Bryant in Summer 2016. Since its upload, it has received 16 views. For similar materials see Calculus in Math at University of Louisiana at Lafayette.
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Date Created: 07/15/16
Calculus I Chapter 2 –Section 2 - Intro to Limits and Properties Review Remember: A limit is not at a number but it is very, very close to that number Therefore, a lim???? ???? = ???? ????→???? Let us start out simple concerning limits, every aspect of math has its starting point. You may be startled when you see the limit symbol in front of the f(x) – function, but don’t worry, think of it has just an f(x) you are evaluating. For Example, in these two equations I going to show you example of the simple limits below: Ex.1: lim 5???? + 9 =? ????→2 (Note: It’s not rocket science. There are simply asking for you to plug in the number, 2 into the function to find out the limit as x goes to 2. Also note that the limit symbol goes way when you reach the step of evaluating) First step and last step: Evaluate. lim 5???? + 9 =? = 5 2 + 9 = 19 ????→2 That’s it! Pretty simple right?! Ok on to the next example… Ex.2:????→2m 4 − ???? =? (Note: The same goes for this problem as well. You will need to plug in the number, -3, as x goes to -3 in order to find the limit.) Step 1: Evaluate. ????→−3 4 − ???? =? = 4 − −3 = 7 ???????? 4 + 3 = 7 - As you can see above, in this function when we have a negative sign and we are subtracting. The negative sign cancels out and causes us to change our sign to a positive sign. See not too bad right?! Now that you got the hang of the simple ones let us move on to some more limits problems that require more work. Don’t worry! It all about the concepts. If you understand the concept of the math game, then it stays pretty simple. Like this for example: 2 ???? − 7???? + 12 ????→3 ???? − 3 You are probably wondering how to solve this problem while trying to recollect your memory of the lecture on limits given by your professor but you can’t, so I will refresh your memory and hopefully it will stick. Notice that if you plug in 3 in the denominator as x goes to 3, you will get 0 in your denominator. Yet despitewhatyougetinthenumeratoryouranswerwillstillbe0.Intherulesofcalculus,whatevernumber in the numeratorover 0 will be undefined, but ifyou can factor to find a definite solutionthatwill beyour limit. Step 1: Factor, if possible. ???? − 7???? + 12 (???? − 4)(???? − 3) ????→3 = ????→3 ???? − 3 ???? − 3 As you can see here, the function in the numerator is factored out. We factored out 2 x’s to give us x squared and we picked to numbers that give us -7 but also give us 12 which is -4 and -3. A negative times a negative gives us a positive number. Well, what do we do? I mean it looks clearer, but can we make it simpler to solve? The answer is YES! There are some like terms and we can cancel them out, which is (x- 3). Step 2: Simplify, if possible. (???? − 4)(???? − 3) lim = lim ???? − 4 ????→3 ???? − 3 ????→3 You can see once we cancel out (x-3), you are only left with x-4 and it gives us no other choice but to evaluate the f(x) in order to find the limit. lim ???? − 4 = 3 − 4 = −1 ????→3 See! It all about solving the puzzle and finding where to plug the pieces right in place and these rules or concepts can help you solve various problems like this by just applying these concepts combined with your algebra skills.
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