Question

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

Limits and continuity
ANSWERED
asked 2021-01-17
Evaluate the following limits.
\(\lim_{(x,y,z)\rightarrow(1,1,1)}\frac{yz-xy-xz-x^2}{yz+xy+xz-y^2}\)

Expert Answers (1)

2021-01-18
Evaluate:
\(\lim_{(x,y,z)\rightarrow(1,1,1)}\frac{yz-xy-xz-x^2}{yz+xy+xz-y^2}\)
Simplification:
We have
\(\lim_{(x,y,z)\rightarrow(1,1,1)}\frac{yz-xy-xz-x^2}{yz+xy+xz-y^2}\)
Apply the limit,
\(\lim_{(x,y,z)\rightarrow(1,1,1)}\frac{yz-xy-xz-x^2}{yz+xy+xz-y^2}=\frac{(1)(1)-(1)(1)-(1)(1)-(1)^2}{(1)(1)+(1)(1)+(1)(1)-(1)^2}\)
\(\frac{1-1-1-1}{1+1+1-1}\)
\(=\frac{-2}{2}\)
\(=-1\)
Hence,
\(\lim_{(x,y,z)\rightarrow(1,1,1)}\frac{yz-xy-xz-x^2}{yz+xy+xz-y^2}=-1\)
3
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...