Suppose that for all x and y the function f satisfies $| f ( x , y ) - 3 | \sqrt { x ^ { 2 } + y ^ { 2 } } \text { and } | f ( x , y ) - 4 | \leq 5 \left( ( x - 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } \right)$ .
Determine, if possible, the values of the following limits.Explain your answer.
Note that the limit may not exist nor be determined from the given information.
(a) $\lim _ { ( x , y ) \rightarrow ( 0 \rho ) } f ( x , y )$ (b) $\lim _ { ( x , y ) \rightarrow ( 4,2 ) } f ( x , y )$

Question

Suppose that for all x and y the function f satisfies $| f ( x , y ) - 3 | > \sqrt { x ^ { 2 } + y ^ { 2 } } \text { and } | f ( x , y ) - 4 | \leq 5 \left( ( x - 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } \right)$ .
Determine, if possible, the values of the following limits.Explain your answer.
Note that the limit may not exist nor be determined from the given information.
(a) $\lim _ { ( x , y ) \rightarrow ( 0 \rho ) } f ( x , y )$ (b) $\lim _ { ( x , y ) \rightarrow ( 4,2 ) } f ( x , y )$

Quizplus · Accepted Answer

The Answer of Suppose that for all x and y the function f satisfies $| f ( x , y ) - 3 | > \sqrt { x ^ { 2 } + y ^ { 2 } } \text { and } | f ( x , y ) - 4 | \leq 5 \left( ( x - 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } \right)$ .
Determine, if possible, the values of the following limits.Explain your answer.
Note that the limit may not exist nor be determined from the given information.
(a) $\lim _ { ( x , y ) \rightarrow ( 0 \rho ) } f ( x , y )$ (b) $\lim _ { ( x , y ) \rightarrow ( 4,2 ) } f ( x , y )$