Question

1. Explain in your own words the meaning of each of the following.

(a) \(\mathop {{\bf{lim}}}\limits_{x \to \infty } f\left( x \right) = {\bf{5}}\)

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

Short answer

(a) When x becomes large, the value of \(f\left( x \right)\) tends to 5.

(b) When x becomes large negatively, the value of \(f\left( x \right)\) tends to 3.

Step-by-step solution

Write the interpretation of the expression in part (a)

The given expression is \(\mathop {\lim }\limits_{x \to \infty } f\left( x \right) = 5\).

The above equation shows that when x becomes large, the value of \(f\left( x \right)\) approach or tends to 5.

Write the interpretation of the expression in part (b)

The given expression is \(\mathop {\lim }\limits_{x \to - \infty } f\left( x \right) = 3\).

The above equation shows that when x becomes large negatively, the value of \(f\left( x \right)\) approach or tends to 3.