Continuty of function

Question

Check the continuity of modulus function at origin i.e |X|

Answer 1

Limit definition of continuity at a point x = a:

If the limit as x approaches a from the left equals the limit as x approaches a from the right and that value is equal to f(a), f is continuous at x =a.

So, for y = |x| at x=0:

limit as x approaches zero from the left is 0.

limit as x approaches zero from the right is also 0.

f(0)=0

Therefore, y=|x| is continuous at (0,0).