Get the answer to "Evaluate the following limits. lim(x,y,z)→(1,1,1)yz−xy−xz−x2yz+xy+xz−y2"

Jaden Easton

Answered question

2021-01-17

Evaluate the following limits.

lim_{(x, y, z) \to (1, 1, 1)} \frac{y z - x y - x z - x^{2}}{y z + x y + x z - y^{2}}

Jozlyn

Skilled2021-01-18Added 85 answers

Evaluate:

lim_{(x, y, z) \to (1, 1, 1)} \frac{y z - x y - x z - x^{2}}{y z + x y + x z - y^{2}}

Simplification:
We have

lim_{(x, y, z) \to (1, 1, 1)} \frac{y z - x y - x z - x^{2}}{y z + x y + x z - y^{2}}

Apply the limit,

lim_{(x, y, z) \to (1, 1, 1)} \frac{y z - x y - x z - x^{2}}{y z + x y + x z - 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) \to (1, 1, 1)} \frac{y z - x y - x z - x^{2}}{y z + x y + x z - y^{2}} = - 1

Jeffrey Jordon

Expert2022-04-01Added 2605 answers

Answer is given below (on video)

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