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

The limit as x approaches-2 of (2-|x|)/(x+2) is 1

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

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

1

Solution steps

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

x

is negative when

x \to - 2

. Therefore

∣ x ∣ = - x

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

Simplify

= x \to - 2 lim (1)

x \to a lim c = c

= 1

What is the limit as x approaches-2 of (2-|x|)/(x+2) ?
The limit as x approaches-2 of (2-|x|)/(x+2) is 1