Why is the following function discontinuous at x=0? f(x)={e^x if x<0 ={x^2 if x>=0

Question

Why is the following function discontinuous at x=0?

f(x)={e^x if x<0

={x^2 if x>=0



(a) f(0) does not exist.

(b) lim x->0 f(x) does not exist (or is infinite).

(c) Both (a) and (b).

(d) f(0) and lim x->0 f(x) exist, but they are not equal.

Answer 1

The answer is b. If we take the limit as we approach 0 from the negative side we get that the limit approaches 1, since e⁰ = 1, but if we take the limit from the right, we get that the limit approaches 0, since 0² = 0. Since the limits from the negative and positive sides are not equal, the function is discontinuous.

Answer 2

Well there you have it ...

same answer from 2 different tutors