tabita57i

2020-11-30

Evaluate the following limits.

$\underset{(x,y,z)\to (1,-1,1)}{lim}\frac{xz+5x+yz+5y}{x+y}$

Arham Warner

Skilled2020-12-01Added 102 answers

We have to find limits of the functions:

$\underset{(x,y,z)\to (1,-1,1)}{lim}\frac{xz+5x+yz+5y}{x+y}$

As it is$\frac{0}{0}$ indeterminate form so solving by factorizing of numerator as well as denominator, we get

$\underset{(x,y,z)\to (1,-1,1)}{lim}\frac{xz+5x+yz+5y}{x+y}=\underset{(x,y,z)\to (1,-1,1)}{lim}\frac{x(z+5)+y(z+5)}{x+y}$

$=\underset{(x,y,z)\to (1,-1,1)}{lim}\frac{(x+y)(z+5)}{(x+y)}$

$=\underset{(x,y,z)\to (1,-1,1)}{lim}(z+5)$

Putting x=1, y=-1, x=1, we get

$=\underset{(x,y,z)\to (1,-1,1)}{lim}(z+5)=(1+5)$

$=6$

Hence, value of limit is 6.

As it is

Putting x=1, y=-1, x=1, we get

Hence, value of limit is 6.

Jeffrey Jordon

Expert2022-04-01Added 2605 answers

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function

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