Hi i'm having a problem with this limit. It seems like it woul be simple to do...
using special trig limits find...
lim 1-cosx / x^2
x->0
i tried breaking it up into 1-cosx/x and 1/x but the 1/x is still undefined.
thanks in advance.
Hi i'm having a problem with this limit. It seems like it woul be simple to do...
using special trig limits find...
lim 1-cosx / x^2
x->0
i tried breaking it up into 1-cosx/x and 1/x but the 1/x is still undefined.
thanks in advance.
$\displaystyle \frac{1-\cos{x}}{x^2} \cdot \frac{1+\cos{x}}{1+\cos{x}} =
$
$\displaystyle \frac{1-\cos^2{x}}{x^2(1 + \cos{x})} =
$
$\displaystyle \frac{\sin^2{x}}{x^2(1 + \cos{x})} =$
$\displaystyle \frac{\sin{x}}{x} \cdot \frac{\sin{x}}{x} \cdot \frac{1}{1+\cos{x}}$
now take the limit.
according to SANDWICH Theory we can replace
$\displaystyle 1-\cos u$
with
$\displaystyle \frac{1}{2} u^2$
when we get ambigious mode of $\displaystyle \frac{0}{0}$
so the menthiond limit can be changed to:
$\displaystyle \lim_ {x\to 0} \frac {\frac {1}{2} x^2}{x^2} = \frac {1}{2}$