Evaluate the following limits. lim_{(x,y,z)rightarrow(1,-1,1)}frac{xz+5x+yz+5y}{x+y}

tabita57i 2020-11-30 Answered
Evaluate the following limits.
lim(x,y,z)(1,1,1)xz+5x+yz+5yx+y
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Expert Answer

Arham Warner
Answered 2020-12-01 Author has 102 answers
We have to find limits of the functions:
lim(x,y,z)(1,1,1)xz+5x+yz+5yx+y
As it is 00 indeterminate form so solving by factorizing of numerator as well as denominator, we get
lim(x,y,z)(1,1,1)xz+5x+yz+5yx+y=lim(x,y,z)(1,1,1)x(z+5)+y(z+5)x+y
=lim(x,y,z)(1,1,1)(x+y)(z+5)(x+y)
=lim(x,y,z)(1,1,1)(z+5)
Putting x=1, y=-1, x=1, we get
=lim(x,y,z)(1,1,1)(z+5)=(1+5)
=6
Hence, value of limit is 6.
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Jeffrey Jordon
Answered 2022-04-01 Author has 2070 answers

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