Evaluate the limit. lim_((x,y,z)->(1,1,1))(x-sqrt(xz)-sqrt(xy)+sqrt(yz))/(x-sqrt(xz)+sqrt(xy)-sqrt(yz))

CheemnCatelvew 2020-10-25 Answered

Evaluate the following limits.
lim(x,y,z)(1,1,1)xxzxy+yzxxz+xyyz

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Expert Answer

crocolylec
Answered 2020-10-26 Author has 100 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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