## kvdop 2 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. pasta

l'Hopitals has taken me back to the start

3. 2le

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. pasta

1/4

5. skywalker94

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. pasta

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. MathPhysics

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