Complete the Table and Use the Result to Estimate $$\lim _ { x \rightarrow - 3 } \frac { x + 3 } { x ^ { 2 } - x - 12 }$$

question 113

Multiple Choice

Complete the table and use the result to estimate $$\lim _ { x \rightarrow - 3 } \frac { x + 3 } { x ^ { 2 } - x - 12 }$$
numerically.
$\begin{array}{|c|c|c|c|c|c|c|c|}\hline x & -3.1 & -3.01 & -3.001 & -3 & -2.999 & -2.99 & -2.9 \\\hline f(x) & & & & ? & & & \\\hline\end{array}$

• A) \(- \frac { 1 } { 7 }\)
• B) 7
• C) \(\infty\)
• D) \(- 7\)
• E) limit does not exist

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Definitions:

Indifference Curves

A graph showing different bundles of goods between which a consumer is indifferent.

Lagrangian

Function to be maximized or minimized, plus a variable (the Lagrange multiplier) multiplied by the constraint.

Lagrange Multiplier

A technique used in constrained optimization problems to find the maximum or minimum of a function subject to constraints.

Lambda

A symbol commonly used in mathematics and physics to represent wavelengths, eigenvalues, and decay constants, among other concepts.