# Thread: Maclaurin and mean value help

1. ## Maclaurin and mean value help

Hi All
i would really appreciate any help on the following problems

1. Maclaurin expansion of lncosx up to x^4.

2. Mean value of y= 2e^x/3 between x=3 and x=6.

Thanks

2. Originally Posted by bhav
Hi All
i would really appreciate any help on the following problems

1. Maclaurin expansion of lncosx up to x^4.

2. Mean value of y= 2e^x/3 between x=3 and x=6.

Thanks
1. Do you know the formula for the nth term in a Maclaurin series? It is in your class notes and textbook. Where are you stuck in applying it?

2. By definition (the one that is in your class notes and textbook): $\displaystyle \displaystyle \frac{\int_{3}^{6} \frac{2 e^x}{3} \, dx}{6 - 3}$

3. First, note that

$\displaystyle \frac{d}{dx}[\ln{(\cos{x})}] = \tan{x}$

so $\displaystyle \ln{(\cos{x})} = \int{\tan{x}\,dx}$.

So if you can find a Maclaurin series for $\displaystyle \tan{x}$, integrate it and then you have the Maclaurin series for $\displaystyle \ln{(\cos{x})}$.