What is the limit as x approaches 5-of (x-5)/(|x-5|) ?

The limit as x approaches 5-of (x-5)/(|x-5|) is -1

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limit as x approaches 5-of (x-5)/(|x-5|)

x \to 5 - lim (\frac{x - 5}{∣ x - 5 ∣})

- 1

Solution steps

x \to 5 - lim (\frac{x - 5}{∣ x - 5 ∣})

x - 5

is negative when

x \to 5 -

. Therefore

∣ x - 5 ∣ = - x + 5

= x \to 5 - lim (\frac{x - 5}{- x + 5})

\frac{x - 5}{- x + 5} = - 1

= x \to 5 - lim (- 1)

x \to a lim c = c

= - 1

\int sinh (x) d x

\frac{d}{d x} ((\frac{x ^{2}}{x ^{3} - 4 x})^{3})

\frac{d}{d x} (\frac{x ^{n}}{n !})

\int_{0}^{π} sin^{4} (2 x) d x

x \to - \infty lim (x \cdot e^{x})

What is the limit as x approaches 5-of (x-5)/(|x-5|) ?
The limit as x approaches 5-of (x-5)/(|x-5|) is -1