find-the-limits-in-exercises-13-20-by-rewriting-the-fractions-first-lim-_x-y-rightarrow11-fracx2-2-x

Question

Find the limits in Exercises $13-20$ by rewriting the fractions first.
$$
\lim _{(x, y) \rightarrow(1,1)} \frac{x^{2}-2 x y+y^{2}}{x-y}
$$

Uma Kumari · Accepted Answer

in this problem here to find the limits, very writing affection. Now we are given that limit. X Y approaches 11 on X is not equal to why X squared minus two weeks. Why less by square over X minus y now, since the numerator and denominator approaches zero as X Y approaches 11 you cannot use the question, too. Now rewriting distractions. We will get limit X Y approaches bandwagon and X is not equal to why we&#x27;ll get X minus y whole square our X minus. Why now? We will use the formula A minus bi whole square is equals toe a square minus two way because the square now using this, we will get limit. Ex lie approaches 11 x minus y and putting the value of X and y as 11 will get one minus one is equals toe zero. Therefore, limit X Y approaches 11 on X is not equal to why X square minus two weeks. Wife plus y squared or X minus Y is it was 20 so there&#x27;s a fine, essential

Uma Kumari · Answer

in this question, we have to find the limits by rewriting the affection. Now we&#x27;re given that limit. X Y approaches 11 and X is not equal toe. Why an X Square minus y squared over X minus life Now relating the affections. The affections approaches 0/0 as X y approaches 11 No, by simplifying it limit X Y approaches 11 and X is not equal toe. Why we will get X minus y x plus why or X minus. Why simplifying it will like limit X y approaches 11 and x plus y. Now, applying the limits, we will get limit X y approaches 11 you will get X Plus y is equals toe one plus one, which is equals to two. Therefore, limit X Y approaches 11 X squared, minus y square or X minus. Why is it was to do so? That&#x27;s the solution

Uma Kumari · Answer

In this problem, you have to find the limits by rewriting the factions. Now we&#x27;re given that Lim X Y approaches bun, bun and X is not equal to while and x y minus Y minus two X plus two over X minus one. Now the objective is to find the value off the limit. Now putting the values off X and Y, we will get limit X y approaches one mine really get one minus one minus two plus 2/1 minus one. Now, by simplifying it, we get 0/0, which is equals toe zero. So the limit cannot be found by direct substitution, which gives indeterminate form now rewriting distraction. We will get Lim X y approaches 11 X is not equal to why will get why x minus one minus two. Multiply X minus one or X minus one now simplifying it were very good. Limit X Y approaches 11 and excess not ableto. Why we get X minus one by minus two over X minus one. Now simplifying it further by canceling the common factor. X minus one. We will get limit. X Y approaches 11 X is not able to why? Why? Minus two? Now apply the limit. X Y approach zero will get limit. Exp i approaches 11 and X is not equal to why we will get one minus two, which is equals toe minus one. Therefore, finally, the limit value exists and limit X Y approaches 11 and X is not equal to why x y minus Y minus two X plus two or X minus one We get it was to minus one. That&#x27;s the final solution.

Uma Kumari · Answer

In this problem, you have to find the limits by rewriting the faction. Now it is given that limit. X Y approaches two and minus four, and why is not equal toe? Fall and X is not equal to X square and by, plus pour over X square. Why? Minus X y plus four X squared, minus four X Now the nominator approaches zero as X Y approaches two and minus four now, but simplifying eight limit X Y approaches to minus four. Why is not equal toe? Fall and X is not equal to X square. We will get by plus four over X y Multiply X minus one plus four eggs. Mollify X minus one. We will get limit X Y approaches to minus four where why is not ableto poor and X is not able to x square Really good. Why plus four over X y plus four x Ex finest one Now with spotter simplifying it. We will get limit X Y approaches to minus four, where y is not equal to four and X is not equal to X square. We will get one or x modify X minus one. Now we&#x27;ll apply the limits limit X Y approaches to minus food. L Y is not equal toe for an X is not equal toe. Explore well, you get one over two multiplied to minus one. We will get 1/2. Therefore, limit X Y approaches to minus four, advising not equal to four and access not ableto X square y plus four over X square Y minus X y plus four X squared minus four X is equal to one hour to that&#x27;s the solution.

Uma Kumari · Answer

in this problem, we have to find the limits by rewriting distraction. Now we&#x27;re given as limit X y approaches to where X plus Why is not equal to four and x plus y minus. Pull over Underwood X Plus y minus two now will proceed as limit. X Y approaches to their X plus y is not ableto fall the right this as under root off X plus y minus two Modify under X plus y plus two Oh, uh, under X plus. Why minus two now simplifying it by canceling the common factors they will get. Limit X y approaches to Underwood X plus Y plus two. Now putting the limits off X and Y don&#x27;t get under Road two plus two plus two By simplifying it, Father, we will get two plus two is equals to four. Therefore, the solution off the human problem that is limit X y approaches toe. The X Plus y is not equal to four x plus y minus four over a little X plus y minus two is equals to four. So there&#x27;s the final solution

Uma Kumari · Answer

in this problem, we have to find the limits by rewriting the fraction were given as limit. X y approaches 20 That two x minus y is not equal to four and under two X minus Y minus two over two X minus Y minus four. Now we can write this as limit X Y approaches 20 The two X minus Y is not equal to four. You can write. This s under two X minus Y minus two. Oh, uh, under rude to x minus Y plus two, multiply the route to X minus Y minus two. Now cancel the non zero factor Our little two x minus Y minus two, and we will get limit X Y approaches to zero one over under two X minus Wife plus who now set X is equal to two and buys equals to zero. We&#x27;ll get one over under. Rude to multiply two minus zero plus two. Nice. By solving this, we will get 1/4. Therefore, the solution off the given problem that is. Limit X Y approaches to zero where two x minus Y is not ableto four and another two x minus Y minus two over two x minus Y minus four is equals toe one or four. There&#x27;s a solution

Problem

Find the limits in Exercises $13-20$ by rewriting…

Problem 13 Easy Difficulty

Find the limits in Exercises $13-20$ by rewriting the fractions first.
$$
\lim _{(x, y) \rightarrow(1,1)} \frac{x^{2}-2 x y+y^{2}}{x-y}
$$

Answer

$\lim _{(x, y) \rightarrow(1,1)} \frac{x^{2}-2 x y+y^{2}}{(x-y)}=0$

Related Courses

Thomas Calculus

Related Topics

Discussion

Top Calculus 3 Educators

Catherine R.

Anna Marie V.

Heather Z.

Samuel H.

Calculus 3 Courses

Vectors Intro

Vector Basics - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 14

Video Transcript

George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano

Thomas Calculus

Catherine R.

Anna Marie V.

Heather Z.

Samuel H.

Vectors Intro

Vector Basics - Example 1

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$\lim _{(x, y) \rightarrow(1,1)} \frac{x^{2}-2 x y+y^{2}}{(x-y)}=0$

Thomas Calculus

Catherine R.

Anna Marie V.

Heather Z.

Samuel H.

Vectors Intro

Vector Basics - Example 1

George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. GiordanoThomas Calculus

Catherine R.

Anna Marie V.

Heather Z.

Samuel H.

George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano

Thomas Calculus