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 9

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

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Definitions:

LIFO Firm

A company that uses the Last-In, First-Out method of inventory valuation where the most recently produced items are sold first.

Net Income

The total earnings of a company after subtracting all expenses, taxes, and costs from total revenue, indicating the company's profit.

LIFO Layers

Different layers or levels within the LIFO inventory method, representing inventory acquired at different times and prices, affecting the calculation of cost of goods sold and ending inventory value.

LIFO Layers

In accounting, layers created under the Last-In, First-Out inventory valuation method, each representing a specific cost associated with inventory purchased at different times.