The discussion revolves around evaluating the limit \(\lim_{x\rightarrow0}\frac{x+\sin x}{2x-\sin 3x}\), specifically focusing on the application of l'Hopital's Rule and alternative methods for solving trigonometric limits.
The discussion is active, with participants sharing their attempts and seeking clarification on concepts. Some guidance has been offered regarding alternative methods to approach the limit, and there is an ongoing exploration of different interpretations of the problem.
Some participants express uncertainty about their knowledge of derivatives and l'Hopital's Rule, indicating that they may not have covered these topics in their studies yet. This suggests a potential gap in foundational understanding that could affect their approach to the problem.
Are you familiar with Taylor series ?mtayab1994 said:Homework Statement
solve the following limit: [tex]\lim_{x\rightarrow0}\frac{x+sinx}{2x-sin3x}[/tex]
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?
mtayab1994 said:No haven't learned it can you fill me on it please?
SammyS said:Are you familiar with Taylor series ?
mtayab1994 said:ok i counted and found the limit to be -2 is that correct?
Dick said: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.