Evaluate the Limit $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { 5 x y ^ { 2 } } { x ^ { 2 } + y ^ { 2 } }$

question 113

Multiple Choice

Evaluate the limit. $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { 5 x y ^ { 2 } } { x ^ { 2 } + y ^ { 2 } }$

• A) the limit does not exist
• B) \(5\)
• C) 2
• D) 0
• E) 1

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Definitions:

Companionate

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Triangular Theory

A theory of love proposed by psychologist Robert Sternberg, which suggests that love can be understood in terms of three components: intimacy, passion, and commitment.

Passionate

Having, showing, or caused by strong feelings or a strong belief.

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Behavior aimed at attracting notice and acknowledgment from others, often due to a desire for validation or affection.