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:

Adipose Tissue

A type of body fat used for storing energy and providing insulation to the body.

Collagen And Elastin

Two structural proteins found in connective tissues in the body, where collagen provides strength and elastin allows elasticity and flexibility.

Extracellular Matrix

A sophisticated mesh of proteins and polysaccharides released by cells that offer both structural and biochemical assistance to adjacent cells.

Loose Connective Tissue

Connective tissue that consists of fibroblasts and fibers scattered in a gel-like matrix.