a-graphically-approximate-the-limit-if-it-exists-by-using-a-graphing-utility-to-graph-the-function-b

Question

(a) graphically approximate the limit (if it exists) by using a graphing utility to graph the function, (b) numerically approximate the limit (if it exists) by using the table feature of a graphing utility to create a table, and (c) algebraically evaluate the limit (if it exists) by the appropriate technique(s).
$$
\lim _{x \rightarrow 1^{-}} \frac{x-1}{x^{2}-1}
$$

Amy Jiang · Accepted Answer

Okay, so we want to find a limit as X approaches one from left of this wall in function here. Well, let&#x27;s go in our denominator. This is a difference of two squares, so we can factor this into an X minus one times the next plus one. Let&#x27;s cancel out our like terms, and I we can use tax up. So here we&#x27;re going to get 1/1 plus one, so that&#x27;s equal to a one half for our limit.

Amy Jiang · Answer

Okay, So for this question, we want to find the limits exactly for 20 from the left of the falling function square root of experts to minus the square root of two over X. Well, let&#x27;s know that if we use division by or if we use jacks up, we have division by zero, so we can&#x27;t use that. So instead, let&#x27;s multiply and divide by the contra gets of or numerator. Okay, so this is going to give us in our new marina, we have the difference of two squares that&#x27;s going to give us on its regal, um, the square root of X plus two squared minus the square root of two squared. So I&#x27;m gonna get exposed to minus a tool which is able to act. So that&#x27;s going to give us X over X times the square root of X plus two plus the square root of two. I don&#x27;t we can count on water like terms, and I&#x27;ll choose duck sub that&#x27;s going to leave us with one over square root of two of the square root of two. So that&#x27;s two square root, too

Amy Jiang · Answer

Okay, so for this question, that&#x27;s solve our following limit directly. So here I&#x27;m gonna multiply by the congregates of our new reader and divided by that since, if we used trucks off, we get the region by zero. So this is going to go most the limits as experts just 16 from the rights of four squared, which is 16 minus x over X minus 16. We can rewrite this as minus 16 minus X times a four plus the square root of X and I Let&#x27;s council Out are like terms now, using tracks over, we have 1/4, plus the square root of 16 and we also have what might assign. So that&#x27;s equal to negative 1/4 plus four. So we get that are limit value is equal to negative born over rates.

Amy Jiang · Answer

Okay, so we want to find are following limit. So here we&#x27;re going to solve this out directly. And you yourself can try this, my graphing on creating a table. So let&#x27;s notice inter denominator. This is a difference of two square so we can practice into a a five minus x times a five plus X. And now let&#x27;s cancel out our like terms and now using Drexel. But we have 1/5 plus five for the rights, so that&#x27;s equal to a one overtime for our limit value.

Amy Jiang · Answer

Okay, so we have to find a limited, like to put this one from the left of X minus one over X squared minus one. Well, we could see an item in a way that we can factor out terms, so if we do that, we get excellent. One over X minus one times X plus one. Now we can camp out of X minus one. And if we use direct substitution, we get one over one plus one, which is you. So our solution is one over two.

Amy Jiang · Answer

Okay, so we have to find the limited default when function. We have a graft out on the inside. You see it at this point right here, too. So if we were to take the limit is particularly in the left hand side, we would get a bit of infinity free. Taken from the right hand side. We would get infinity. Well, we know that you will listen up. Same. So we know that Fisher are limited to two of our fallen functions does not exist.

Problem

(a) graphically approximate the limit (if it exis…

Problem 49 Easy Difficulty

Answer

Part A: 5
Part B: 5
Part C: 1$/ 2$
See explanation for graph and table.

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Part A: 5Part B: 5Part C: 1$/ 2$See explanation for graph and table.

Precalculus with Limits

Catherine R.

Anna Marie V.

Heather Z.

Samuel H.

Integration Review - Intro

Definite vs Indefinite

Ron Larson, Robert Hostetler, Bruce H. EdwardsPrecalculus with Limits

Catherine R.

Anna Marie V.

Heather Z.

Samuel H.

Part A: 5
Part B: 5
Part C: 1$/ 2$
See explanation for graph and table.

Ron Larson, Robert Hostetler, Bruce H. Edwards

Precalculus with Limits