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

f(0) is defined as zero so it's not A

the limit does not exist because the one-sided

limits do not agree...

from the left, the limit is 1

from the right, the limit is 0

option C is eliminated because A is false

option D is elimianted because the limit

does not exist

as I said before, the limit does not

exist because the one sided limits

do not agree

answer is B