Complete the Table and Use the Result to Estimate $\lim _{x \rightarrow-2} \frac{x+2}{x^{2}-x-6}$

question 23

Multiple Choice

Complete the table and use the result to estimate $\lim _{x \rightarrow-2} \frac{x+2}{x^{2}-x-6}$ numerically.

$\begin{array}{|c|c|c|c|c|c|c|c|}\hline x & -2.1 & -2.01 & -2.001 & -2 & -1.999 & -1.99 & -1.9 \\\hline f(x) & & & & ? & & & \\\hline\end{array}$

• A) \( -\frac{1}{5} \)
• B) 5
• C) \( \infty \)
• D) -5
• E) limit does not exist

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Definitions:

Dissociative Disorders

A group of mental disorders characterized by a disconnection and lack of continuity between thoughts, memories, surroundings, actions, and identity.

Schizophrenia

A chronic and severe mental disorder that affects how a person thinks, feels, and behaves, characterized by delusions, hallucinations, and disordered thinking.

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A group of mental health disorders characterized by significant feelings of anxiety and fear, impacting daily functioning.

Delusions

False beliefs that are maintained even though they clearly are out of touch with reality.