# Using limits to find other limits

• Sep 18th 2009, 04:58 PM
zeda234
Using limits to find other limits
Hello everyone,
I am not completely sure of how to approach this problem:

If lim f(x)/x^2 as x-->0 is equal to 5, find the following limits:

a) lim f(x) as x--> 0
b) lim f(x)/x as x--> 0

Any suggestions would be appreciated.
Thank you !
• Sep 18th 2009, 05:07 PM
skeeter
Quote:

Originally Posted by zeda234
Hello everyone,
I am not completely sure of how to approach this problem:

If lim f(x)/x^2 as x-->0 is equal to 5, find the following limits:

what would f(x) have to be for the above limit to be true?

a) lim f(x) as x--> 0
b) lim f(x)/x as x--> 0

...
• Sep 18th 2009, 05:11 PM
zeda234
Quote:

Originally Posted by skeeter
...

So in order for the statement to be true, it is necessary to eliminate the x^2 in the denominator right? Otherwise you would be dividing by zero. So could f(x) be 5(x^2)? This way the x^2 would divide out and 5 would be left?
Am I on the right track?
• Sep 18th 2009, 05:12 PM
skeeter
Quote:

Originally Posted by zeda234
So in order for the statement to be true, it is necessary to eliminate the x^2 in the denominator right? Otherwise you would be dividing by zero. So could f(x) be 5(x^2)? This way the x^2 would divide out and 5 would be left?
Am I on the right track?

... keep going (Clapping)
• Sep 18th 2009, 05:15 PM
zeda234
Quote:

Originally Posted by skeeter
... keep going (Clapping)

Ok. So...

(a) lim 5(x^2) as x-->0

(b)lim 5(x^2)/x as x-->0

So then both answers are zero?
• Sep 18th 2009, 05:28 PM
skeeter
Quote:

Originally Posted by zeda234
Ok. So...

(a) lim 5(x^2) as x-->0

(b)lim 5(x^2)/x as x-->0

So then both answers are zero?

you figure out what f(x) must be on your own ... why then do you doubt your solutions to these two simple limits?
• Sep 18th 2009, 05:30 PM
zeda234
Quote:

Originally Posted by skeeter
you figure out what f(x) must be on your own ... why then do you doubt your solutions to these two simple limits?

The textbook I have used a different method for a similar question earlier on and it looks far more complicated. So I just wasn't sure if guessing was correct. Therefore, both answers are indeed zero right? (Smirk)
• Sep 18th 2009, 05:34 PM
Krizalid
yes.