Hi again cousinit!
I assume here that with /x/ you imply the "absolute value of x". If
this assumption is wrong, please let me know through a clarification
request.
In order to answer this question, it's best to examine first what the
/ / (absolute value) operator does to a number x. If x is greater than
zero, then the // operator returns the same number x. If x is smaller
than zero (negative) then the // operator returns -x. For example, if
x=-1, then /x/=-(-1)=1. Check the following link:
Absolute Value definition
http://mathworld.wolfram.com/AbsoluteValue.html
In this case, we have that x goes to 0 from the "left"; so x is
smaller than zero. Therefore, since x is smaller than zero, then
/x/=-x. So we can repalce this fact into the function to get:
Lim 8x Lim 8x Lim 8x
x->0- ----------- = x->0- ----------- = x->0- ----
3x + /x/ 3x + (-x) 2x
Finally, we can just cancel out the x's (it doesn't matter that the
denominator goes to zero, you can cancel these terms because they are
not exactly zero, but they are rather "very close" to zero. So we get
that the limit you're looking for is 8/2.
I hope this helps! If you have any doubts regarding my answer, please
don't hesitate to request a clarification before rating it. Otherwise
I await your rating and final comments.
Best wishes!
elmarto |
