What is the limit as x approaches-5 of (5-|x|)/(5+x) ?

The limit as x approaches-5 of (5-|x|)/(5+x) is 1

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limit as x approaches-5 of (5-|x|)/(5+x)

x \to - 5 lim (\frac{5 - ∣ x ∣}{5 + x})

1

Solution steps

x \to - 5 lim (\frac{5 - ∣ x ∣}{5 + x})

x

is negative when

x \to - 5

. Therefore

∣ x ∣ = - x

= x \to - 5 lim (\frac{5 - ( - x )}{5 + x})

Simplify

= x \to - 5 lim (1)

x \to a lim c = c

= 1

What is the limit as x approaches-5 of (5-|x|)/(5+x) ?
The limit as x approaches-5 of (5-|x|)/(5+x) is 1