What is the limit as x approaches 2 of (x-2)/(|x-2|) ?

The limit as x approaches 2 of (x-2)/(|x-2|) is diverges

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limit as x approaches 2 of (x-2)/(|x-2|)

x \to 2 lim (\frac{x - 2}{∣ x - 2 ∣})

diverges

Solution steps

x \to 2 lim (\frac{x - 2}{∣ x - 2 ∣})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 2 + lim (\frac{x - 2}{∣ x - 2 ∣}) = 1

x \to 2 - lim (\frac{x - 2}{∣ x - 2 ∣}) = - 1

= diverges

\int sin (2 x) e^{(3 x)} d x

y \to 0 lim (\frac{0}{y ^{2}})

\frac{1}{( s + 1 ) ( s + 3 ) ^{2}}

\int \frac{x ^{3} + 6 x ^{2} + 2 x + 3}{x ^{2} + 6 x + 1} d x

What is the limit as x approaches 2 of (x-2)/(|x-2|) ?
The limit as x approaches 2 of (x-2)/(|x-2|) is diverges