# Question about continuity of a function...? Q: Find points where function is discontinuous:f(x)= x/|x|Function is f(x)= x divided by modulus of xPlz tell me its solution with step by step...?Plz tell me as soon as possible...?

## Expert Answers

The continuity of a function, at a certain point, happens when the left hand limit of the function is equal to the right hand limit of the function at that point. These limits must be equal to the value of function at that point.

Notice that the questionable point is x = 0.

`lim_(x-gt0)x/|x| = lim_(x-gt0) (xlt0)1/|-1| = -1`  (use l'Hospital's theorem)

`lim_(x-gt0)x/|x| = lim_(x-gt0) (xgt0)1/|1| = 1`

Since the left hand limit `!=`  right hand limit, the function is discontinuous at x = 0.

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