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

question 29

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:

Decomposer

Organisms that break down dead or decaying organisms, contributing to the nutrient cycle by recycling nutrients back into the ecosystem.

Earth's Surface

The outermost layer of the Earth, consisting of the crust and the upper part of the mantle.

Estuaries

Coastal water bodies where freshwater from rivers meets and mixes with saltwater from the ocean, creating unique and richly biodiverse environments.