Find the Limit $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { \sin \left( 9 x ^ { 2 } + 9 y ^ { 2 } \right) } { 7 x ^ { 2 } + 7 y ^ { 2 } }$

question 116

Multiple Choice

Find the limit $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { \sin \left( 9 x ^ { 2 } + 9 y ^ { 2 } \right) } { 7 x ^ { 2 } + 7 y ^ { 2 } }$ Hint: If $x = r \cos \theta$ and $y = r \sin \theta ,$ then $( x , y ) \rightarrow ( 0,0 )$ if and only if $r \rightarrow 0 ^ { + }$

• A) \(\frac { 9 } { 7 }\)
• B) \(1\)
• C) \(0\)
• D) \(\frac { 7 } { 9 }\)

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Definitions:

Endocrine System

A network of glands that produce and release hormones directly into the blood to regulate the body's growth, metabolism, and sexual development and function.

Ductless Glands

Glands that release hormones directly into the bloodstream without using ducts, also known as endocrine glands.

Peripheral Nervous System

The part of the nervous system that consists of the nerves and ganglia outside of the brain and spinal cord.

Somatic

Pertaining to or affecting the body, especially as distinct from the mind or psyche.