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