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