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Find the limits in Exercises $13-20$ by rewriting the fractions first.$$\lim _{(x, y) \rightarrow(4,3)} \frac{\sqrt{x}-\sqrt{y+1}}{x-y-1}$$
$\frac{1}{4}$
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, 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's a solution.
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