Question

Find the limit or show that it does not exist.

33. \(\mathop {lim}\limits_{x \to - \infty } \left( {{x^2} + 2{x^7}} \right)\)

Short answer

The value of the limit is \( - \infty \).

Step-by-step solution

Use the property of limit

A function is continuous at a point “a” if \(\mathop {\lim }\limits_{x \to a} f\left( x \right) = f\left( a \right)\)

Evaluate the given limit

Evaluate the given limits as follows:

\(\begin{aligned}\mathop {\lim }\limits_{x \to - \infty } \left( {{x^2} + 2{x^7}} \right){\rm{ }} &= {\left( { - \infty } \right)^2} + 2{\left( { - \infty } \right)^7}\\ &= {\infty ^2} - 2{\infty ^7}\\ &= - \infty \end{aligned}\)

Thus, the value of the limit is \( - \infty \).