Math Snap

STEP 1

Assumptions1. We are finding the limit as x approaches negative infinity.
. The function is $\frac{x^{6}-3 x^{4}}{ x^{}- x+1}$

STEP 2

We divide the numerator and the denominator by $x^{6}$, the highest power of x in the numerator.
$$\lim{x \rightarrow-\infty} \frac{x^{6}- x^{4}}{2 x^{2}-2 x+1} = \lim{x \rightarrow-\infty} \frac{1-\frac{}{x^{2}}}{\frac{2}{x^{4}}-\frac{2}{x^{5}}+\frac{1}{x^{6}}}$$

STEP 3

As x approaches negative infinity, the terms with x in the denominator will approach0.
$$\lim{x \rightarrow-\infty} \frac{1-\frac{3}{x^{2}}}{\frac{2}{x^{}}-\frac{2}{x^{5}}+\frac{1}{x^{6}}} = \frac{1-0}{0-0+0}$$

Calculate the limit.
$$\frac{1-0}{0-0+0} = \frac{1}{0}$$The limit as x approaches negative infinity of the function $\frac{x^{6}-3 x^{4}}{2 x^{2}-2 x+1}$ is undefined because we cannot divide by zero.