Evaluate the following limits. \(\displaystyle\lim_{{{\left({x},{y},{z}\right)}\rightarrow{\left({1},{1},{1}\right)}}}{\frac{{{x}-\sqrt{{{x}{z}}}-\sqrt{{{x}{y}}}+\sqrt{{{y}{z}}}}}{{{x}-\sqrt{{{x}{z}}}+\sqrt{{{x}{y}}}-\sqrt{{{y}{z}}}}}}\)

palmantkf4u 2022-03-30 Answered
Evaluate the following limits.
lim(x,y,z)(1,1,1)xxzxy+yzxxz+xyyz
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Answers (1)

sorrisi7yny
Answered 2022-03-31 Author has 9 answers
Given:
lim(x,y,z)(1,1,1)xxzxy+yzxxz+xyyz
On simplification, we get:
lim(x,y,z)(1,1,1)xxzxy+yzxxz+xyyz=lim(x,y,z)(1,1,1)x(xz)y(xz)x(xz)+y(xz)
=lim(x,y,z)(1,1,1)(xz)(xy)(xz)(x+y)
=lim(x,y,z)(1,1,1)(xy)(x+y)
(11)(1+1)
=0
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