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# The Table Method Math 210

University of Louisiana at Lafayette

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This 3 page Class Notes was uploaded by Cynthia Ndulaka on Monday July 18, 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 10 views. For similar materials see Calculus in Math at University of Louisiana at Lafayette.

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Date Created: 07/18/16

Calculus 1 Chapter 2, Section 2 – Intro to Limits (cont.) and Their Properties Prior to this, were learning how to solve limits as x approaches a number analytically with use of algebra, but now we are going to look at how to solve a limit using a table method. Don’t worryit is not anything hard, it concludesofmaking a table andwriting down close numbers to the leftandrightofthe limitandpluggingthosevaluesto findvaluesthatdrawclosetothelimit.Thisapretty simple method to follow. Let’s look at an example which we can solve for the limit using the table method: Ex.1: ???? − 7???? + 12 ????(????) = lim =? ????→3 ???? − 3 First, we must find what make the f(x)= 0, which is 3 as x approaches 3 the whole function becomes 0, so in our table when x is at 3, it will be undefined. The key note is that a limit is not at a value but a close to that value. Now that know that the f(x)=0 at 3, we must find numbers to left of 3 (less than 3) like 2, and values much closer like 2.9 and 2.99. Also find numeric values closest to 3 on the right side (greater than 3) as well in order to set up our table like 3.01, 3.1 and 4. Step 1: Set up table with the following x-values. x 2 2.9 2.99 3 3.01 3.1 4 F(x) Step 2: Plug in the remaining values by plugging in the x-values into the equation above to find the limit. x 2 2.9 2.99 3 3.01 3.1 4 F(x) -2 -1.1 -1.01 DNE -1.01 -1.1 -2 -As you can see as we get closer to 3 from the left and right, we are getting closer to -1 and that is our limit. See it was not that bad as long as you master the concept. Let try another to make sure you got the hang of it. Ex.2: ???? − 1 ???? ???? = l????→1 ???? − 1 According to the following f(x), we need to find the value that makes the f(x) =0, which is 1 as x goes to 1. We must choose numbers close to the 1 from the left and right. From the left, we can choose numbers closest to 1 such as0.9,0.99 and 0.999. Also from theright, the numeric values closest to 1 such as1.001, 1.01 and 1.1. Step 1: Set up a table with the following values mentioned above. x 0.9 0.99 0.999 1 1.001 1.01 1.1 f(x) Step 2: Plug in the remaining values by plugging in the x-values into the equation above to find the limit. x 0.9 0.99 0.999 1 1.001 1.01 1.1 f(x) 2.71 2.97 2.999 DNE 3.001 3.03 3.31 As we get closer to 1, we find out that we are getting closer to 3 from the left and right side. Therefore, 3 is our limit. See that was not too bad! Let try another example just to make sure we have mastered the limit by using the table method. Ex.3: ???? ???? = lim ???? ????→0 √???? + 1 − 1 According to the f(x), we need to find the numeric value that makes f(x) =0, which is numerical value, 0. We need to find numbers from the left and right. From the left side of 0, we can use numerical values such as -0.1,-0.01,-0.001. Also from the right side of 0, we can use the 0.001, 0.01 and 0.1. Step 1: Set up a table with the following values mentioned above. x -0.1 -0.01 -0.001 0 0.001 0.01 0.1 f(x) Step 2: Plug in the remaining values by plugging in the x-values into the equation above to find the limit. x -0.1 -0.01 -0.001 0 0.001 0.01 0.1 f(x) 1.95 1.995 1.9995 DNE 2.0005 2.005 2.05 As you get closer to the number 0, the values from the left and right side are getting closer from the numerical value, 2. Therefore, our limit is 2. Overall, the table method is just another way of finding a limit.

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