Solving trigonometric limits

mtayab1994

1. Homework Statement

solve the following limit: $$\lim_{x\rightarrow0}\frac{x+sinx}{2x-sin3x}$$

3. The Attempt at a Solution

I know the principle of solving all sorts of limits but not trig limits, and since we just started trig limits it's still not clear to me, but i think to solve it we have to separate it then solve but i don't know. Any help on how to start please?

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Dick

Homework Helper
Do you know l'Hopital's rule?

mtayab1994

No haven't learned it can you fill me on it please?

SammyS

Staff Emeritus
Homework Helper
Gold Member
1. Homework Statement

solve the following limit: $$\lim_{x\rightarrow0}\frac{x+sinx}{2x-sin3x}$$

3. The Attempt at a Solution

I know the principle of solving all sorts of limits but not trig limits, and since we just started trig limits it's still not clear to me, but i think to solve it we have to separate it then solve but i don't know. Any help on how to start please?
Are you familiar with Taylor series ?

Better yet:
multiply by (1/x) over (1/x) .​

Dick

Homework Helper
No haven't learned it can you fill me on it please?
You may not have covered it yet so you may be expected to do it a different way. Divide the numerator and denominator by x. Now you probably do know the limit sin(x)/x. Try to use that to find the limits of the terms.

mtayab1994

Are you familiar with Taylor series ?
No sorry i'm not familiar with taylor series, but i know that for l'hospital's rule we have to take the derivative of the numerator and the derivative of the denominator; but i have never learned derivatives so i can't do that. Is it possible to solve it some other way?

mtayab1994

Ok the derivative of x+sinx is cosx+1 and how about the bottom?

mtayab1994

ok i counted and found the limit to be -2 is that correct?

Dick

Homework Helper
ok i counted and found the limit to be -2 is that correct?
Yes, if you used l'Hopital then you might check whether that is allowed. Otherwise you should try doing it using that the limit of sin(x)/x is 1.

mtayab1994

Yes, if you used l'Hopital then you might check whether that is allowed. Otherwise you should try doing it using that the limit of sin(x)/x is 1.
Yea thank you very much I get the trick. It's the same for almost all of them.