how do you find the asymptotes of a curve like:
where the denominator is a power for eg.
and why do you integrate to get 3lnx and not ??
help very appreciated thanks!!
how do you find the asymptotes of a curve like:
where the denominator is a power for eg.
and why do you integrate to get 3lnx and not ??
help very appreciated thanks!!
To get the asymptotes, test its end behaviors by taking both limits as and as . Both of which are 0, therefore there is only one asymptote which is .
To answer your second question, the reason it turns into is because when you are integrating using the reverse power rule which says
however this only works if , because then denominator becomes 0. In your case, we have , so so it doesn't work. So we use . Make sure that it's absolute value of x and not just regular x. If you don't put the absolute value signs, you'll get it wrong.
Cheers!