Calculus Examples

$lim_{x \to \frac{π}{2}} - \frac{1}{6} \tan (x)$

Step 1

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

$lim_{x \to {(\frac{π}{2})}^{-}} - \frac{1}{6} \tan (x)$

Step 2

Since the function $\tan (x)$ approaches $\infty$ , the negative constant $- \frac{1}{6}$ times the function approaches $- \infty$ .

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Step 2.1

Consider the limit with the constant multiple $- \frac{1}{6}$ removed.

$lim_{x \to {(\frac{π}{2})}^{-}} \tan (x)$

Step 2.2

As the $x$ values approach $\frac{π}{2}$ from the left, the function values increase without bound.

$\infty$

Step 2.3

Since the function $\tan (x)$ approaches $\infty$ , the negative constant $- \frac{1}{6}$ times the function approaches $- \infty$ .

$- \infty$