Calculus Examples

$lim_{x \to 0} 2 \cot (x)$

Step 1

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

$lim_{x \to 0^{-}} 2 \cot (x)$

Step 2

Since the function $\cot (x)$ approaches $- \infty$ , the positive constant $2$ times the function also approaches $- \infty$ .

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Step 2.1

Consider the limit with the constant multiple $2$ removed.

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

Step 2.2

As the $x$ values approach $0$ from the left, the function values decrease without bound.

$- \infty$