2-4-52
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OK, so we want the limit as X goes to zero from the right.
Zero from the right would give us square root of X.
So sqrt 0 is just zero.
I used this equation 'cause it said from the right.
Now, if we want the limit as X goes to zero from the left of X
^2 sine 1 / X, we're going to rewrite this so that we have our
signed portions by themselves and we're going to put
everything else down at the end.
Now, if I have 1 / X as my angle here, I need to have 1 / X in
the denominator.
If I put 1 / X in the denominator, you're going to
tell me we have to put 1 / X in the numerator.
If there is no value in this denominator down here, it's
understood to be over one.
So now we have the limit as X goes to zero from the left of
sign 1 / X / 1 / X times the limit as X goes to zero from the
left of plain old X because X ^2 / X reduces, so we get 1 * 0 or
zero.
What can we say about the limit as X approaches zero of F of X?
We can say it's got to equal 0 because the left side and the
right side have the same limit value.