How to Solve Trigonometric Limits Using l'Hopital's Rule

[mtayab1994]

Homework Statement

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

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?

 

[Dick]

Do you know l'Hopital's rule?

 

[mtayab1994]

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

 

[SammyS]

Homework Statement

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

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 ?

Added in Edit:

Better yet:

multiply by (1/x) over (1/x) .​

 

[Dick]

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]

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.