# Math Help - Limits of Trig Functions

1. ## Limits of Trig Functions

...again.

1. lim sec x - 1 / xsecx (x--->0)
2. lim (1-cosx)^2 / x (x--->0)
3. lim 5x / sin 4x (x--->0)

Sometimes I get these, and sometimes I don't. Is there any specific way I'm supposed to look at these trig. functions? I keep getting marked off for the way I've been solving them. =/

Any help is greatly appreciated!

1. lim sec x - 1 / xsecx (x--->0)
2. lim (1-cosx)^2 / x (x--->0)
3. lim 5x / sin 4x (x--->0)
1) Multiply up & down by $\cos x$

2) Use that $(1-\cos x)^2=(1-\cos x)(1-\cos x)$

3) Classic, there're many types of these ones, just use the fact $\lim_{x\to0}\frac{\sin x}x=1$

3. Thanks!

The last one, I know I have to use sin x/x = 1, but every time I use that to justify my answer...I get marked off. ...

$\lim_{x\to0}\frac{5x}{\sin4x}=\frac54\lim_{x\to0}\ frac{4x}{\sin4x}$