find-the-limits-in-exercises-13-20-by-rewriting-the-fractions-first-lim-_x-y-rightarrow22-fracxy-4sq

Question

Find the limits in Exercises $13-20$ by rewriting the fractions first.
$$
\lim _{(x, y) \rightarrow(2,2)} \frac{x+y-4}{\sqrt{x+y}-2}
$$

Uma Kumari · Accepted 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

Uma Kumari · Answer

in this problem, you find the limits very rarely confection. Now we&#x27;re given as limit X y approaches 00 where X is not equal to what and X minus. Why plus two under root X minus two under. Why? Oh uh, a node X minus. And why now we&#x27;ll evaluate the following limit limit X Y approaches 00 x is not equal to buy. We will get under x all square minus under Waibel Square plus two under root X minus two under rule by all our I know X minus. I know why now, using the formula another ex whole square minus and the wife will square is equals to another X minus another. Why MaliVai Under X plus another. Why Very good limit. X y approaches 00 where X is not equal to y By using the AB a formula we will get under root X minus Underwood Why multiply and Arab X plus another Why plus two MaliVai a little X minus and why? Oh uh, another X minus. And why now? By simplifying it further, we will get limit. X y approaches 00 They&#x27;re X is not equal to why will get another old eggs less a little. Why less too? Now setting X equals to zero and buys It was 20 We will get another zero plus Underwood zero plus two, and we finally get to therefore the solution off the given problem that is limit X approaches 00 x is not equal to why x minus y plus 200 X minus 200 y or on the X minus. Understood, why is equals two, So that&#x27;s a final solution.

Uma Kumari · Answer

in this problem, we have to find the limits. Very dating affection we were given as limit. Ex Way Approaches 43 and X is not equal to y plus one and Underwood X minus under y plus one Oh X minus Y minus one. Now we can write this as limit X Y Approaches 43 where X is not equal toe white plus one as egg under eggs minus under y plus one over X minus Y plus one. Now for the simplifying aid limit. X Y approaches 43 under the eggs minus our little white plus one. Oh Lord under X minus under white list one. Multiply under root X plus under Y plus one. Now cancel the non zero factor that is the X minus under Y plus one, we will get limit X Y approaches 43 one over another route. Eggs plus under Y plus one. Now applying the limit will get one over under four plus under four, but is equals to 1/4. Therefore, the required solution off the even problem that is limit X y. Approaches 43 where X is not equal toe y plus one Underwood X minus Underwood Y plus one over X minus Y minus one is equals toe one or four, so there&#x27;s a 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 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

Problem

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

Problem 18 Easy Difficulty

Find the limits in Exercises $13-20$ by rewriting the fractions first.
$$
\lim _{(x, y) \rightarrow(2,2)} \frac{x+y-4}{\sqrt{x+y}-2}
$$

Answer

4

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