Question

Explain the meaning of each of the following.

(a)\(\mathop {{\bf{lim}}}\limits_{x \to - {\bf{3}}} f\left( x \right) = \infty \)

(b)\(\mathop {{\bf{lim}}}\limits_{x \to {{\bf{4}}^ + }} f\left( x \right) = - \infty \)

Short answer

(a) The expression shows when x is approaching \( - 3\), the value of f will become arbitrarily large.

(b) The expression shows when x is approaching 4 from the right-hand side, f will become arbitrarily large, negatively.

Step-by-step solution

Step 1:Interpretation of the equation in (a)

Theequation\(\mathop {\lim }\limits_{x \to - 3} f\left( x \right) = \infty \)represents that as x is approaching to\( - 3\), the value of \(f\left( x \right)\) will become arbitrarily large.

Interpretation of the equation in (b)

The equation \(\mathop {\lim }\limits_{x \to {4^ + }} f\left( x \right) = - \infty \) represents that as x is approaching to 4 from the right side, the value of \(f\left( x \right)\) will become arbitrarily large, negatively.