Question:
is the function defined by f(x)=|x|, a continuous function
Answer:
Yes, the function f(x) = |x|, x = 0 is continuous
LHL:
Limx->0- f(x) = Limx->0- |x| = Limh->0 |0-h| = Limh->0 |-h| = Limh->0 (h) = 0
RHL:
Limx->0+ f(x) = Limx->0+ |x| = Limh->0 |0+h| = Limh->0 |h| = Limh->0 (h) = 0
and f(0) = 0
Since Limx->0- f(x) = Limx->0+ f(x) = f(0)
So, the function f(x) = |x|, x = 0 is continuous
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