## anonymous 4 years ago Find the lim of tan(2x)/(3x+sinx) as x approaches 0

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1. NoelGreco

I don't see any quick way without l'Hopital.

2. anonymous

l'Hopitals has taken me back to the start

3. anonymous

If l'Hopital doesn't work the first time but gives you the condition for it again, you can repeat it. You might have better luck the second time around.

4. anonymous

1/4

5. anonymous

One way is to use l'Hopital, but a faster way is to use the linear approximations for sine and tangent. The answer is 1/2.

6. anonymous

THE DIFFERENTIAL IS SEC^2(X)/3+COS(x).numerator is 1 and denominator is 4 answer is 1/4 how did you get 1/2??????

7. anonymous

pasta! skywalker94 is right! Using l'Hopital, we'll get 1/2. $\lim_{x \rightarrow 0}(\tan2x/(3x+sinx))=\lim_{x \rightarrow 0}[2(1+\tan^{2}2x)/(3+cosx)]=1/2$

8. anonymous

use expansion method it is the fastest.... tanx = x + x^3/3............sinx = x - x^3/3!

9. anonymous

and from that the ans is 1/2 Math Physics and skywalker ur right..!!!!

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