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

tabita57i

tabita57i

Answered question

2020-11-30

Evaluate the following limits.
lim(x,y,z)(1,1,1)xz+5x+yz+5yx+y

Answer & Explanation

Arham Warner

Arham Warner

Skilled2020-12-01Added 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.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-04-01Added 2605 answers

Answer is given below (on video)

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