$\text { Find } \lim _ { ( x , y ) \rightarrow ( a , b ) } \left[ \frac { f ( x , y ) + g ( x , y ) } { f ( x , y ) } \right] \text { by using the limits } \lim _ { ( x , y ) \rightarrow ( a , b ) } f ( x , y ) = 5 \text { and }$ $\lim _ { ( x , y ) \rightarrow ( a , b ) } g ( x , y ) = 6$
A) $\frac { 6 } { 5 }$
B) $\frac { 5 } { 11 }$
C) $\frac { 5 } { 6 }$
D) $\frac { 11 } { 6 }$
E) $\frac { 11 } { 5 }$

Question

Quizplus · Accepted Answer

The limit of the given expression as $(x, y) \rightarrow (a, b)$ simplifies to $\frac{5 + 6}{5}$ using the provided limits, which equals $\frac{11}{5}$.

lim⁡(x,y)→(a,b)g(x,y)=6\lim _ { ( x , y ) \rightarrow ( a , b ) } g ( x , y ) = 6lim(x,y)→(a,b)​g(x,y)=6

$\lim _ { ( x , y ) \rightarrow ( a , b ) } g ( x , y ) = 6$