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

Question

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

Arham Warner · Accepted Answer

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 · Accepted Answer

Answer is given below (on video)

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

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