Find the following limit: lim_{(x,y)rightarrow(3,3)}(frac{x-y}{sqrt x-sqrt y})

sibuzwaW 2021-02-21 Answered
Find the following limit:
lim(x,y)(3,3)(xyxy)
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Expert Answer

faldduE
Answered 2021-02-22 Author has 109 answers
Given:
lim(x,y)(3,3)(xyxy)
On putting the limits directly, we get:
lim(x,y)(3,3)(xyxy)=00
On further solving the equation, we have:
lim(x,y)(3,3)(xyxy)=lim(x,y)(3,3)((x)2(y)2xy)
Since,
a2b2=(ab)(a+b)
Therefore,
lim(x,y)(3,3)((xy)(x+y)xy)
lim(x,y)(3,3)(x+y)
Now putting the limits, we get:
(3+3)
=23
The required answer.
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Jeffrey Jordon
Answered 2022-04-01 Author has 2070 answers

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