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

Zoe Oneal

Zoe Oneal

Answered question

2021-02-05

Evaluate the following limits.
lim(x,y,z)(1,1,1)x2+xyxzyzxz

Answer & Explanation

wornoutwomanC

wornoutwomanC

Skilled2021-02-06Added 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.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-24Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?