### Home > CALC > Chapter Ch3 > Lesson 3.2.1 > Problem 3-44

3-44.

Evaluate.

Before finding the limit, factor the numerator and the denominator. If the '0' in the denominator cancels out, then the limit exists.

For all limits as *x* →∞, you are looking for end behavior. For example, is there a horizontal asymptote? Or does the function approach +∞ or −∞ in the end? To answer this question, compare the highest power in the numerator with the highest power in the denominator.

Highest power in the numerator: *x*^{2}

Highest power in the denominator: *x*^{2}

Note: this means that *f*(*x*) has a horizontal asymptote of *y* = 1.

First, factor the expression. Visualize the left-hand and right-hand limits of the simplified function. Do they match up?

You can prove this by showing that

Limit does not exist.