Find the limit $\lim _ { ( x , y , z ) \rightarrow ( 3,2,4 ) } \frac { x y + y z + x z } { x y z - 6 }$
A) $\frac { 13 } { 9 }$
B) $0$
C) $- \frac { 1 } { 6 }$
D) $\frac { 1 } { 6 }$

Question

Quizplus · Accepted Answer

The limit is $\frac { 13 } { 9 }$ because the numerator and denominator both approach 0 as $( x , y , z ) \rightarrow ( 3,2,4 )$, but the numerator approaches 0 faster than the denominator.

Find the Limit lim⁡(x,y,z)→(3,2,4)xy+yz+xzxyz−6\lim _ { ( x , y , z ) \rightarrow ( 3,2,4 ) } \frac { x y + y z + x z } { x y z - 6 }lim(x,y,z)→(3,2,4)​xyz−6xy+yz+xz​

Find the Limit $\lim _ { ( x , y , z ) \rightarrow ( 3,2,4 ) } \frac { x y + y z + x z } { x y z - 6 }$