Question

examine the continuity of given function at x=0.
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Answer 1

Answer:

At x=0

LHL f(0-h) = lim. 0-h

h-> 0. |0-h|

= 0-0

|0-0|

= 0

RHL f(0+h) = lim. 0+h

h->0 |0+h|

= 0+0

|0+0|

= 0

f(0) = 0

so, LHL=RHL= F(x)

hence, function is continuous at x=0