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 -1

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

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

- 1

Solution steps

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

x - 2

is negative when

x \to 2 -

. Therefore

∣ x - 2 ∣ = - x + 2

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

\frac{x - 2}{- x + 2} = - 1

= x \to 2 - lim (- 1)

x \to a lim c = c

= - 1

y^{^{'}} = \frac{( 3 x ^{2} - e ^{x} )}{2 y - 5}

y^{^{''}} + 11 y^{^{'}} + 30 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\int_{1}^{4} 3 x e^{x} d x

\int_{1}^{5} \frac{ln ( R )}{R ^{2}} d R

\frac{\partial}{\partial x} (- \frac{1}{x ^{2}})

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 -1