Limits of Trig Functions

**alreadyinuse** · September 12th 2007, 06:51 PM

...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!

**Krizalid** · September 12th 2007, 06:55 PM

Originally Posted by alreadyinuse

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 $\lim_{x\to0}\frac{\sin x}x=1$

**alreadyinuse** · September 12th 2007, 07:15 PM

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. ...

**Krizalid** · September 12th 2007, 07:18 PM

Originally Posted by alreadyinuse

3. lim 5x / sin 4x (x--->0)

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

That's all

**alreadyinuse** · September 12th 2007, 07:22 PM

That's exactly what I did on my last quiz and she still marked me off. Hmmm. I think I'll just ask her exactly what she wants from me, heh.

Thanks a ton!

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