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

question 63

Multiple Choice

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.
Select the correct answer.

• A) \(a = 15\), limit equals \(- 0.6\)
• B) \(a = 15\), limit equals \(0.6\)
• C) \(a = - 15\), limit equals \(0.6\)
• D) \(a = - 15\), limit equals \(- 0.6\)
• E) \(a = 15\), limit equals 18

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Definitions:

Modus Tollens

A logical argument form that suggests if a implies b, and b is found to be false, then a must also be false.

Antecedent

An event, condition, or cause that logically or temporally precedes another; in grammar, the noun or noun phrase that a pronoun refers to.

Inductive Reasoning

A method of reasoning in which general principles are inferred from specific observations, moving from particular instances to broader generalizations.