Calculus Examples

$lim_{x \to 0} x^{3} \cot (x)$

Step 1

Consider the left sided limit.

$lim_{x \to 0^{-}} x^{3} \cot (x)$

Step 2

Make a table to show the behavior of the function $x^{3} \cot (x)$ as $x$ approaches $0$ from the left.

$\begin{array}{c} x & x^{3} \cot (x) \\ - 0.1 & 0.00996664 \\ - 0.01 & 0.00009999 \\ - 0.001 & 0.000001 \end{array}$

Step 3

As the $x$ values approach $0$ , the function values approach $0$ . Thus, the limit of $x^{3} \cot (x)$ as $x$ approaches $0$ from the left is $0$ .

$0$

Step 4

Consider the right sided limit.

$lim_{x \to 0^{+}} x^{3} \cot (x)$

Step 5

Make a table to show the behavior of the function $x^{3} \cot (x)$ as $x$ approaches $0$ from the right.

$\begin{array}{c} x & x^{3} \cot (x) \\ 0.1 & 0.00996664 \\ 0.01 & 0.00009999 \\ 0.001 & 0.000001 \end{array}$

Step 6

As the $x$ values approach $0$ , the function values approach $0$ . Thus, the limit of $x^{3} \cot (x)$ as $x$ approaches $0$ from the right is $0$ .

$0$