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
(2abs(x))/(2+x), which I will assume is the correct form.
f(x) = (2abs(x))/(2+x)
is the same as
f(x)=(2x)/(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