Question

Discuss the continuity of the function at a x=0​

Answer 1

Answer:

Here, f(x) may be defined for 'x' not equal to 0 is as-

when x<0;

LHL = lim(x→0) (2|x|+x^2)/x

= lim(x→0) (-2x+x^2)/x

= -2

when x≥0;

RHL = lim(x→0) (2x+x^2)/x

= 2

Here, LHL is not equal to RHL

Hence, f(x) is not continuous at x=0...