Question

$\lim_{x \to 0} \frac{1}{x}$

Answer 1

Does not exist

Answer 2

To evaluate the limit $\lim_{x \to 0} \frac{1}{x}$, we need to consider the behavior of the function $f(x) = \frac{1}{x}$ as $x$ approaches 0 from both the left side and the right side.

Left-hand limit: $\lim_{x \to 0^-} \frac{1}{x} = -\infty$

As $x$ approaches 0 from values less than 0, the value of $\frac{1}{x}$ becomes a large negative number, tending towards negative infinity.

Right-hand limit: $\lim_{x \to 0^+} \frac{1}{x} = +\infty$

As $x$ approaches 0 from values greater than 0, the value of $\frac{1}{x}$ becomes a large positive number, tending towards positive infinity.

Since the left-hand limit and the right-hand limit are not equal, the limit $\lim_{x \to 0} \frac{1}{x}$ does not exist.