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

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

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

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

1

Solution steps

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

x

is negative when

x \to - 2 -

. Therefore

∣ x ∣ = - x

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

Simplify

= x \to - 2 - lim (1)

x \to a lim c = c

= 1

x \to 0 lim (\frac{sin ( x ) + x}{x})

x \to 0 + lim (2 x csc (2 π - x))

x \to 2 lim (4 - 2 x)

x \to 0 lim (- \frac{1}{∣ x ∣})

x \to 1 - lim (ln (ln (x)))

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