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:

Body Mass Index (BMI)

A numerical computation that evaluates an individual's weight in relation to their height, used as an indicator of obesity and underweight.

Medium Frame

A body type that falls between a small and large build, often determined by wrist circumference and height.

Desired Weight

The weight an individual aims to achieve or maintain, often through diet and exercise.

Overweight

A condition defined by having a body mass index (BMI) over the normal weight range for one's height, often leading to increased health risks.