Suppose That for All X and Y the Function F $| f ( x , y ) - 3 | > \sqrt { x ^ { 2 } + y ^ { 2 } } \text { and } | f ( x , y ) - 4 | \leq 5 \left( ( x - 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } \right)$

question 37

Essay

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) $\lim _ { ( x , y ) \rightarrow ( 4,2 ) } f ( x , y )$

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Regulations governing the amount of interest that can be charged on a loan, intended to prevent lenders from imposing excessively high interest rates.

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A legal maximum price that can be charged for a good or service, typically set by government to protect consumers.

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A government or regulatory imposed minimum price above the equilibrium price, preventing prices from dropping too low.

Usury Laws

Regulations designed to protect consumers by capping the interest rate that lenders can charge on credit.