Limits and the Horizontal Asymptote. True or False question?

if the limit of f(x) as x-%26gt;infinity is infinity and the limnit of g(x) as x-%26gt;infinity is infinity, then the limit of f(x)/g(x) as x-%26gt;infinity does not exist.





true or false?





my guess is it is true because there is a horizontal asymptote there. am i right?Limits and the Horizontal Asymptote. True or False question?
well, let's take f(x)=g(x)=x for x%26gt;0.


we have f-%26gt;inf and g-%26gt;inf as x-%26gt;inf,


but f/g is always 1, and f/g -%26gt; 1 as x-%26gt;inf.Limits and the Horizontal Asymptote. True or False question?
then go show my example to the teacher... x/x tends to 1, because it is always 1 (except at x=0), even though x goes to infinity.


An answer (yes/no, true/false) isn't enough, there must be a proof. If your teacher can't disproof my proof, then you know where you're at...

Report Abuse

In other words, my example is a counterexample to the proposition you gave.

Report Abuse

mortgage