Given f is an odd function that is f(-x) =-f(x).
And [tex]Lim_{x->0+} f(x) = 3[/tex]
[tex]Lim_{x->0-} f(x) =?[/tex]
Let x=-a
As x->0- , a->0+
So, [tex]Lim_{x->0-} f(x) = Lim_{a->0+} f(-a)[/tex]
= [tex]Lim_{a->0+} (-f(a))[/tex] (Since f(-a)=-f(a) for odd function)
= [tex]-Lim_{a->0+} f(a) = -3[/tex]
Hence [tex]Lim_{x->0-} f(x) = -3[/tex]
Answer: we should have that:
[tex]\lim_{x \to \--0} f(x) = -3[/tex]
Step-by-step explanation:
We know that f(x) is an odd function, this means that f(-x) = -f(x)
We know that:
[tex]\lim_{x \to \++0} f(x) = 3[/tex]
this means that wen we aproximate to zero for the right (the positive side) we have that the value is.
First, this tell us that f(x) can not be a continue function, because of the fact that is odd we will have that when we aproximate the same lim but from the negative side, we will have that:
[tex]\lim_{x \to \--0} f(x) = -3[/tex]
