Thread: 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 !

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

...

Originally Posted by skeeter

...

Thanks for your reply.
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?

Originally Posted by zeda234

Thanks for your reply.
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

Originally Posted by skeeter

... keep going

Ok. So...

(a) lim 5(x^2) as x-->0
The answer is zero then?

(b)lim 5(x^2)/x as x-->0
The answer is also zero?

So then both answers are zero?

Originally Posted by zeda234

Ok. So...

(a) lim 5(x^2) as x-->0
The answer is zero then?

(b)lim 5(x^2)/x as x-->0
The answer is also zero?

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?

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?

yes.