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

question 89

Multiple Choice

Find the limit $\lim _ { ( x , y ) \rightarrow ( 0,0 ) } \frac { \sin \left( 9 x ^ { 2 } + 9 y ^ { 2 } \right) } { 2 x ^ { 2 } + 2 y ^ { 2 } }$ . 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) \(\frac { 9 } { 2 }\)
• B) 0
• C) \(\frac { 2 } { 9 }\)
• D) 1

---

Definitions:

Working Capital

A measure of a company's liquidity, operational efficiency, and short-term financial health, calculated as current assets minus current liabilities.

Current Ratio

A financial indicator used to assess whether a company can handle its obligations in the short term, calculated by the ratio of current assets to current liabilities.

Acid-Test Ratio

A liquidity metric that measures a company's ability to pay off its current liabilities with its quick assets without relying on inventory sales.

Times Interest Earned

A financial metric that measures a company's ability to meet its debt obligations by comparing its interest expenses to its earnings before interest and taxes (EBIT).