Suppose that f and g are real functions such that , as .
Prove that as approaches infinity.
What (if anything) can be said in general about the difference , the product and the quotient as ??
Justify any assertions that you make.
Suppose that f and g are real functions such that , as .
Prove that as approaches infinity.
What (if anything) can be said in general about the difference , the product and the quotient as ??
Justify any assertions that you make.
I was thinking that since it means that for any arbitary , there exsists a such that , similarly since , it means that for any arbitary , there exsists a such that .
But i dont really know were to go from here.
So if we let and , we have :
and
And we have and
So for both arbitrary A>0 and B>0, we have an arbitrary , such that for all x > j (that is > k and > h) we have f(x)>A and f(x)>B, that is f(x)>C
the red parts give you the definition of
Note : this is not really a formal proof, it's just giving you the idea.
yes! true! that is why they are inconclusive because you HAVE 3 POSSIBLE outcomes AS IT IS.. (actually, there are only two.. either the limit does or does not exist..)
but if you manipulate it (i mean if you are given with specific functions), you will find THE ONLY and the RIGHT outcome.