Limits of Trig Functions

1. Apr 19, 2005

erik05

Hello all. I missed a class in calculus so I didn't get the notes on this so if anyone could explain this question for me, it would be much appreciated.

$$\lim_{x \rightarrow 0} \frac {tanx}{4x}$$
$$= \frac {sinx}{cos4x} ?$$

Not really too sure if I manipulated the equation right. Any hints for the next step? Thanks.

2. Apr 19, 2005

Gmaximus

You can't do that!!!!!

Use l'hopitals rule.

$$\lim_{x \rightarrow 0} \frac {tanx}{4x} =\lim_{x \rightarrow 0} \frac {secxtanx}{4}$$

3. Apr 19, 2005

erik05

Sorry, I haven't learned l'hopitals rule yet and we're not suppose to use it for these questions.

4. Apr 19, 2005

vincentchan

expand tanx in taylor series, and do what you should do....

5. Apr 19, 2005

erik05

This is going to sound really pathetic but no, we haven't the taylor series either.

6. Apr 19, 2005

vincentchan

do you know the fact that
$$\lim_{x \rightarrow 0} \frac {sinx}{x} =1$$
if yes, you should start from here

7. Apr 19, 2005

dextercioby

I think Taylor series is taught way after l'Hôpital's rule,don't u think so?

Daniel.

8. Apr 19, 2005

erik05

That I do know.

9. Apr 20, 2005

dextercioby

What about "tangent's" definition...?And the limit of cosine as its argument goes to 0 ?

Daniel.

10. Apr 20, 2005

leon1127

= 1/4*(sin[x]/x)*(sec[x])

11. Apr 20, 2005

erik05

Ah...I got it. Thanks all.

12. Apr 20, 2005

Orion1

Limit Laminate...

Solution:
$$\boxed{\lim_{x \rightarrow 0} \frac {\tan x}{4x} = \frac{1}{4}}$$

Last edited: Apr 20, 2005
13. Apr 20, 2005

dextercioby

How fancy that \boxed{...},too bad u don't know "\tan"...

Daniel.

P.S.BTW,I've searched Mathworld and A & S,couln't find this $tanx$ function...

P.P.S.Neither $sinx$,nor $secxtanx$,but i found $\mbox{sinc}\ x$... :surprised

P.P.P.S.You edited...

Last edited: Apr 20, 2005