Thread: Infinity limits

I'm suppose to solve for c and n.
Could someone please give me some advice on how to start ?
Any advice/hints are greatly appreciated.

For rational functions the limit at + or - infinity is the ratio of the highest
powered terms.

This should be enough to answer the question.

Originally Posted by Calculus26

For rational functions the limit at + or - infinity is the ratio of the highest
powered terms.

This should be enough to answer the question.

Could you explain it a litte bit more please? I don't understand.

looking at the ratio you have of highest powered terms you have

lim(10*x^7)/(cx^n) = 10/10 = 1

what do c and n have to be?

Originally Posted by Calculus26

looking at the ratio you have of highest powered terms you have

lim(10*x^7)/(cx^n) = 10/10 = 1

what do c and n have to be?

I got it ! Thanks its 10 and 7. But why do we just ignore everything else?

the key is at infinity

limc/x^n = 0

if you divide through by the highest poweed terms everything goes to 0 except the leading terms

for Eg

lim(2x^3 + 3x + 1)/(x^3 +2)

=lim [x^3( 2 + 3/x^2 +1/x^3)/[x^3(1+2/x^3)]

=lim (2+3/x^2 +1/x^3)/(1+ 2/x^3)

= (2+0+0)/(1+0) = 2

so imsteas of dividing through by the highest powered terms each time we recognize we can just consider the ratio of highest powered term.

This is also true if the highest powers on top and bottom are different just consider the ratio