Posted by **thomas** on Sunday, October 4, 2009 at 3:39pm.

can someone help me determine that limit for the following function, as x --> -2?

2 - abs(x) / 2 + x

- calculus - limits -
**MathMate**, Sunday, October 4, 2009 at 3:58pm
Please be sure to enclose numerators and denominators in parentheses when transcribing fractions. The given expression does not equal to

(2-abs(x))/(2+x), which I will assume is the correct form.

f(x) = (2-abs(x))/(2+x)

is the same as

f(x)=(2-x)/(2+x) when x∈[0,∞)

f(x)=(2+x)/(2+x) when x∈(-∞,-2)∪(-2,0)

As x→-2,

f(x)=(2+x)/(2+x)

which equals 1 by long division.

Therefre

Lim x→-2 f(x) = 1

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