lim (x^-4 - 2x^-2 - 3x^-1-2)/(7x^-3 - 6x^-2 + 3) as x->0
You asked:
Evaluate the expression: \(\lim_{x \to 0}{\frac{{x}^{-4} - 2 \cdot {x}^{-2} - 3 \cdot {x}^{-1} - 2}{7 \cdot {x}^{-3} - 6 \cdot {x}^{-2} + 3}}\)
MathBot Answer:
The two-sided limit \(\lim_{x \to 0}{\frac{{x}^{-4} - 2 \cdot {x}^{-2} - 3 \cdot {x}^{-1} - 2}{7 \cdot {x}^{-3} - 6 \cdot {x}^{-2} + 3}}\) does not exist because the directional limits from the right and the left result in different values.
Right limit:
\(\displaystyle\lim_{x \to 0^+}\left(\frac{-2 - \frac{3}{x} - \frac{2}{x^{2}} + \frac{1}{x^{4}}}{3 - \frac{6}{x^{2}} + \frac{7}{x^{3}}}\right) = \infty\)
Left limit:
\(\displaystyle\lim_{x \to 0^-}\left(\frac{-2 - \frac{3}{x} - \frac{2}{x^{2}} + \frac{1}{x^{4}}}{3 - \frac{6}{x^{2}} + \frac{7}{x^{3}}}\right) = -\infty\)