Question

Enamine the continuity of the function
5x 2x
0
sin 3x
atx=0​

Answer 1

The absolute value function is continuous at 0.

Since |x| = -x for all x < 0, we find the following left hand limit. Since the two one-sided limits agree, the two sided limit exists and is equal to 0, and we find that the following is true. ... In fact, the absolute value function is continuous (on its entire domain R).