limits to infinity (1 Viewer)

[Abiloey]

lim x ->infinity of (9+x^2)/(3x)
Go !

 

[tommykins]

if you split the fractoins, you get

9/3x + x^2/3x = 3/x + x/3 so as x ->infinity 3/x -> 0 and x/3 -> infinity

 

[copeys]

I was always told to "divide by the highest power of x, if that fails, divide by the next highest"

I divided by the highest power of x and got like 1/0 which doesn't work.

I then divided by x:



Cancelling down, then substituting x=infinity in, I got:



Which cancels down to:



Is that right?

 

[ComingUpForAir]

you can do it a number of ways, but yea answer is 'infinity'

 

[ninetypercent]

yes. divide by the highest power of x in the denominator

 

[cutemouse]

If the limit is infinity then no limit exists.

 

[chrisrules]

yes. divide by the highest power of x in the denominator

2 years of ext 1 maths and i wasn't told this.

thankyou

 

[ninetypercent]

2 years of ext 1 maths and i wasn't told this.

thankyou

what!!! are u serious?

 

[Lukybear]

Its in cambridge. I wasnt taught this either.

 

[Trebla]

You can sorta tell intuitively that the limit will not exist because the squared term in the numerator magnifies x much more than the x in the denominator as x gets large, so the dominating effect is that the numerator becomes large, hence the expression blows up to infinity...