Question

f(x) = |x|={x,x>=0
{-x,x<0
Find lim f(x)
x-> 0

Answer 1

Answer:

0

Explanation:

$f(x) = |x| \\ \lim_{x \to0 {}^{ + } } |x| = \lim_{x \to0 {}^{ + } } x = 0 \\ \lim_{x \to0 {}^{ - } } |x| = \lim_{x \to0 {}^{ - } } ( - x) = 0 \\ f(0) = 0 \\ so \\ f(0) = \lim_{x \to0 {}^{ + } } f(x) = \lim_{x \to0 {}^{ - } } f(x) = 0$