Evaluate the following limits. lim_{(x,y,z)rightarrow(1,1,1)}frac{x^2+xy-xz-yz}{x-z}

Zoe Oneal 2021-02-05 Answered
Evaluate the following limits.
lim(x,y,z)(1,1,1)x2+xyxzyzxz
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Expert Answer

wornoutwomanC
Answered 2021-02-06 Author has 81 answers
We have to evaluate the limit of the function with three variable:
lim(x,y,z)(1,1,1)x2+xyxzyzxz
After putting value of limit we get that it is 00 form
We can solve this limit by laws of factorization.
Solving by factorization,
lim(x,y,z)(1,1,1)x2+xyxzyzxz=lim(x,y,z)(1,1,1)x2xz+xyyzxz
=lim(x,y,z)(1,1,1)x(xz)+y(xz)xz
=lim(x,y,z)(1,1,1)(xz)(x+y)(xz)
=lim(x,y,z)(1,1,1)(x+y)
=1+1
=2
Hence, value of given limit is 2.
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