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

x \to 0 - lim (x e^{- \frac{1}{x}})

x \to 0 lim (\frac{6 ^{x} - 6 ^{- x}}{x})

x \to 0 lim (x^{2} \frac{1}{x ^{2}})

x \to 0 lim (\frac{( 2 - x ) ^{- 1} - 2 ^{- 1}}{x})

x \to 0 lim (\frac{1 - cos ( 2 x )}{x sin ( 2 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 -1