Calculus Examples

$lim_{x \to - \frac{π}{2}} \frac{\tan (x)}{\frac{15}{2 x - π}}$

Step 1

Simplify the limit argument.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$lim_{x \to - \frac{π}{2}} \tan (x) \frac{2 x - π}{15}$

Step 1.2

Combine $\tan (x)$ and $\frac{2 x - π}{15}$ .

$lim_{x \to - \frac{π}{2}} \frac{\tan (x) (2 x - π)}{15}$

Step 2

Consider the left sided limit.

$lim_{x \to {(- \frac{π}{2})}^{-}} \frac{\tan (x) (2 x - π)}{15}$

Step 3

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

$- \infty$

Step 4

Consider the right sided limit.

$lim_{x \to {(- \frac{π}{2})}^{+}} \frac{\tan (x) (2 x - π)}{15}$

Step 5

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

$\infty$

Step 6

Since the left sided and right sided limits are not equal, the limit does not exist.

$Does not exist$