Calculus Examples

$lim_{x \to 0} \cos (\frac{1}{x})$

Change the two-sided limit into a right sided limit.

$lim_{x \to 0^{+}} \cos (\frac{1}{x})$

Make a table to show the behavior of the function $\cos (\frac{1}{x})$ as $x$ approaches $0$ from the right.

$\begin{array}{c} x & \cos (\frac{1}{x}) \\ 0.1 & - 0.83907152 \\ 0.01 & 0.86231887 \\ 0.001 & - 0.92173957 \\ 0.0001 & - 0.92173957 \end{array}$

As the $x$ values approach $0$ , the function values approach $- 0.922$ . Thus, the limit of $\cos (\frac{1}{x})$ as $x$ approaches $0$ from the right is $- 0.922$ .

$- 0.922$