limits

rmn · #1 $Old$ September 18th, 2007, 06:42 PM

if the lim of f(X)/x^(2)=1 as x approaches -2, find lim f(x) as x approaches -2 and lim f(x)/x as x approaches -2

I have no idea how to do this >< isn't it 1??

ThePerfectHacker · #2 $Old$ September 18th, 2007, 06:46 PM

Quote:

Originally Posted by rmn $View Post$

if the lim of f(X)/x^(2)=1 as x approaches -2, find lim f(x) as x approaches -2 and lim f(x)/x as x approaches -2

I have no idea how to do this >< isn't it 1??

$\lim_{x\to -2} \frac{f(x)}{x^2} = 1$

Then,
$\lim_{x\to -2} \frac{f(x)}{x} = \lim_{x\to -2} \frac{f(x)}{x^2} \cdot x = (1)(-2) = -2$

Then,
$\lim_{x\to -2}f(x) = \lim_{x\to -2}\frac{f(x)}{x^2} \cdot x^2 = (1)(-2)^2 = 4$

Jhevon · #3 $Old$ September 18th, 2007, 06:49 PM

Quote:

Originally Posted by rmn $View Post$

if the lim of f(X)/x^(2)=1 as x approaches -2, find lim f(x) as x approaches -2 and lim f(x)/x as x approaches -2

I have no idea how to do this >< isn't it 1??

$\lim_{x \to -2} \frac {f(x)}{x^2} = \lim_{x \to -2} \frac {f(x)}{4} = 1$

$\Rightarrow \frac 14 \lim_{x \to -2}f(x) = 1$

now continue

rmn · #4 $Old$ September 18th, 2007, 06:51 PM

thanks, so we should multiply it by something that will get rid of the x and make it what we're looking for? and then substitute?