Find the Limit $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { \sin \left( 9 x ^ { 2 } + 9 y ^ { 2 } \right) } { 6 x ^ { 2 } + 6 y ^ { 2 } }$

question 135

Short Answer

Find the limit $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { \sin \left( 9 x ^ { 2 } + 9 y ^ { 2 } \right) } { 6 x ^ { 2 } + 6 y ^ { 2 } }$ . Hint: If $x = r \cos \theta$ and $y = r \sin \theta$ , then $( x , y ) \rightarrow ( 0,0 )$ if and only if $r \rightarrow 0 ^ { + }$ .

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Definitions:

Angular Gyrus

A region of the brain located in the parietal lobe, involved in processing language, numbers, and spatial cognition, among other functions.

Cortex

The outer layer of the cerebrum of the brain, involved in complex functions including memory, attention, perception, cognition, awareness, thought, language, and consciousness.

Reading

The process of recognizing and understanding the meaning of symbols and characters in written or printed material.

Corpus Callosum

The large band of neural fibers connecting the two hemispheres of the brain, facilitating communication and coordination between them.