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

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

Calculus 3

Calculus 1 / AB

Chapter 14

Partial Derivatives

Section 2

Limits and Continuity in Higher Dimensions

Applications of the Derivative

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In this problem, you have to find the limits by rewriting the factions. Now we'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's the final solution.

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