Is There a Number $a$ Such That $\lim _ { x \rightarrow - 3 } \frac { 3 x ^ { 2 } + a x + a + 3 } { x ^ { 2 } + x - 6 }$

question 37

Short Answer

Is there a number $a$ such that $\lim _ { x \rightarrow - 3 } \frac { 3 x ^ { 2 } + a x + a + 3 } { x ^ { 2 } + x - 6 }$ exists? If so, find the value of $a$ and the value of the limit.

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Definitions:

Equilibrium Quantity

The quantity of goods or services supplied equals the quantity demanded at the market equilibrium price.

Economic Welfare

The overall health and well-being of an economy, measured by factors such as wealth, happiness, and the distribution of resources.

Rent Controls

A restriction set by authorities on how much landlords can demand for renting out houses or apartments.

Long Run

An economic term for a timeframe in which all factors of production and costs are variable, allowing for full adjustment to changes.