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:

Australopithecus Species

A group of extinct hominids closely related to humans, known for walking upright and living millions of years ago.

Sequence

An ordered list of elements or events that follow a specific pattern or arrangement.

Homo Erectus

An extinct species of hominid that lived from the end of the Pliocene epoch to the early Pleistocene, known for being one of the first to use fire and simple tools.

Homo Habilis

An extinct species of early human that lived in Africa, known for using stone tools.