# Thread: Using limits to find other limits

1. ## 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 !

2. 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
...

3. 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?

4. 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

5. Originally Posted by skeeter
... keep going
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?

6. Originally Posted by zeda234
Ok. So...

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

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