Use the method of your choice to evaluate the following limits. lim_{(x,y)rightarrow(1,1)}frac{x^2+xy-2y^2}{2x^2-xy-y^2}

Clifland 2021-01-10 Answered
Use the method of your choice to evaluate the following limits.
lim(x,y)(1,1)x2+xy2y22x2xyy2
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Expert Answer

Dora
Answered 2021-01-11 Author has 98 answers
Given:
lim(x,y)(1,1)x2+xy2y22x2xyy2
To evaluate:
The given limit.
Solution:
Here,
lim(x,y)(1,1)x2+xy2y22x2xyy2
On simplifying the equation,
The required equation is,
lim(x,y)(1,1)x2+xy2y2x2xy2y2=lim(x,y)(1,1)x+2y2x+y
Plug in the values (x,y)=(1,1)
lim(x,y)(1,1)x2+xy2y2x2xy2y2=1+2×12×1+1
lim(x,y)(1,1)x2+xy2y2x2xy2y2=1+22+1
lim(x,y)(1,1)x2+xy2y2x2xy2y2=33
lim(x,y)(1,1)x2+xy2y2x2xy2y2=1
Which is required.
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Jeffrey Jordon
Answered 2022-04-01 Author has 2087 answers

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