Homework Statement
I need to know the greatest n for which n! is greater or equal to x, and the greatest n for which nlgn is greater or equal to x.
Homework Equations
Can't think of any. Sorry!
The Attempt at a Solution
For a "normal" function, like, say, lgn or n^2, it would be...
Homework Statement
I have a problem with McLaurin series. I never know when to stop. How do I know if O(x3) is adequate, or O(x5)?
Let's take this exam question as an example.
\lim_{x \to 0} \frac{(x+1)e^x -1-2x}{cosx-1}
\frac{(x+1)e^x -1-2x}{cosx-1} = \frac{(x+1)(1+x+\frac{x^2}{2!}+...)...
Cyosis - got it, thanks!
g_edgar - I agree, but the example was taken from an old exam and what I wrote in the first post was the only answer or explanation given in the solutions. I don't know if a solution taking two cases would have given full credit.
Hm.
\frac{d}{dx} e^x = e^x \frac{d}{dx} x
and
\frac{d}{dx} ln|x| = \frac{1}{x}
so
\frac{d}{dx} e^{x \log|x+2|} = e^{x \log|x+2|} \frac{d}{dx}(x \log|x+2|) = e^{x \log|x+2|} (ln|x+2| + \frac{x}{x+2}) = |x+2|^x (ln|x+2| + \frac{x}{x+2})
Thanks for the tip, I would never have thought of...
Solved! d/dx |x+2|^x
Homework Statement
I need someone to explain this:
http://www.dafydd.se/stuff/solvethis.png [Broken]
Homework Equations
I guess the following are of relevance...
\frac{d}{dx} |x| = \frac{x}{|x|}
\frac{d}{dx} a^x = a^x ln a
The Attempt at a Solution
The...