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

Appreciate the evolutionary perspective on emotion and its expression.

Recognize the differences in emotional expression and perception among genders.

Understand the concept of emotional learning and its mechanisms.

Identify factors influencing individual differences in emotional expression and perception.

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Definitions:

Negative Thought

A thought that is usually pessimistic, critical, or self-defeating, often contributing to feelings of distress.

Aaron Beck

An American psychiatrist who is known as the father of cognitive therapy, focusing on changing clients' patterns of thinking to reduce negative emotions.

Bipolar Disorder

A mental health condition characterized by extreme mood swings that include emotional highs (mania or hypomania) and lows (depression).

Depressive Symptoms

Manifestations of depression, including persistent sadness, lack of interest, changes in appetite or sleep, and feelings of worthlessness.