Calculus Examples

$lim_{x \to 180} {0.3}^{\cot (x)}$

Step 1

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

$lim_{x \to 180^{-}} {0.3}^{\cot (x)}$

Step 2

Move the limit into the exponent.

${0.3}^{lim_{x \to 180^{-}} \cot (x)}$

Step 3

Make a table to show the behavior of the function $\cot (x)$ as $x$ approaches $180$ from the left.

$\begin{array}{c} x & \cot (x) \\ 179.9 & 0.91598657 \\ 179.99 & 0.76269667 \\ 179.999 & 0.74855798 \\ 179.9999 & 0.74715462 \\ 179.99999 & 0.74701439 \end{array}$

Step 4

As the $x$ values approach $180$ , the function values approach $0.747$ . Thus, the limit of $\cot (x)$ as $x$ approaches $180$ from the left is $0.747$ .

${0.3}^{0.747}$

Step 5

Raise $0.3$ to the power of $0.747$ .

$0.40682682$