niyazikeklk
New member
- Joined
- Sep 15, 2020
- Messages
- 1
Please use "English" for communication at this forum.
Prof, what you stated above via a-c only shows that the limit at x=a exists. To show continuity at x= a I am sure that you know that you also need to have d) x→alimf(x)=f(a)A function, f(x), is continuous at x= a if and only if
a) x→a+limf(x) exists
b) x→a−limf(x) exists
c) x→a+limf(x)=x→a−limf(x).
So what are x→a+limf(x)=x→0lim0 and x→a−limf(x)=x→0lim(x2)asinb(x2)?
(It helps to know that x→0limxsin(x)=1.)
Yes, the last line should have beenProf, what you stated above via a-c only shows that the limit at x=a exists. To show continuity at x= a I am sure that you know that you also need to have d) x→alimf(x)=f(a)