Question

Suppose that f is an odd function of x. Does knowing that modifyingbelow lim with x right arrow 0 superscript plus f left parenthesis x right parenthesisequals3 tell you anything about modifyingbelow lim with x right arrow 0 superscript minus f left parenthesis x right parenthesis​? Give reasons for your answer.

Answer 1

Answer: we should have that:

$\lim_{x \to \--0} f(x) = -3$

Step-by-step explanation:

We know that f(x) is an odd function, this means that f(-x) = -f(x)

We know that:

$\lim_{x \to \++0} f(x) = 3$

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:

$\lim_{x \to \--0} f(x) = -3$

Answer 2

Given f is an odd function that is f(-x) =-f(x).

And $Lim_{x->0+} f(x) = 3$

$Lim_{x->0-} f(x) =?$

Let x=-a

As x->0- , a->0+

So, $Lim_{x->0-} f(x) = Lim_{a->0+} f(-a)$

                         = $Lim_{a->0+} (-f(a))$   (Since f(-a)=-f(a) for odd function)

                         = $-Lim_{a->0+} f(a) = -3$

Hence $Lim_{x->0-} f(x) = -3$