Calculus Examples

$lim_{x \to 5} - (\frac{- 5}{x - 5} + 5)$

Step 1

Combine terms.

Tap for more steps...

Step 1.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{x - 5}{x - 5}$ .

$lim_{x \to 5} - (\frac{- 5}{x - 5} + \frac{5 (x - 5)}{x - 5})$

Step 1.2

Combine the numerators over the common denominator.

$lim_{x \to 5} - \frac{- 5 + 5 (x - 5)}{x - 5}$

Step 2

Consider the left sided limit.

$lim_{x \to 5^{-}} - \frac{- 5 + 5 (x - 5)}{x - 5}$

Step 3

As the $x$ values approach $5$ from the left, the function values decrease without bound.

$- \infty$

Step 4

Consider the right sided limit.

$lim_{x \to 5^{+}} - \frac{- 5 + 5 (x - 5)}{x - 5}$

Step 5

As the $x$ values approach $5$ 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.

$Does not exist$