This is my first post. I have a slight problem. I know how to solve this exercise but there's something different here :/.
Ok, so i need to demonstrate this inequality by applying Lagrange's theorem on [k, k+1] interval, i have the solution in my book but the theorem i know is f ' (c) = [f(k+1) - f(k)]/(k + 1 - k), instead the book says its the other way around f(k) - f(k+1) ... etc
So if some1 can solve this problem for me from scratch ... i'd be grateful.
Thanks, for the poster above me, i know where i made my mistake, forgot the minus sign from the derivative of f(x) :shy:
Here's how i solved it:
I'm on my last year of high-school ... i have my exams in a week, im not from the US or UK and i don't know how the theorems sound like in english (or the maths terminology in english)
Hey, i decided to post my math problems here instead of making a bunch of "little" topics, that'd be messy, i hope you don't mind this.
And here i am with a new problem:
I know that f(x) is monotonically increasing for x < 0, and monotonically decreasing for x > 0, f(0) = 1, f(1) = f(-1) = 1/4
Please don't think i registered on this forum just so you can make my homework, it's not my homework, i'm trying to learn for the exam (SAT equiv. in the US), i have the book with all the variants, 100 in number, the exam is 7 days, and i still have some "minor" exercises from all those 100 variants.
First off: the rule in this forum is, no more than two problems per thread. You should move this problem. It's for your benefit as much as anyone else's. People are less likely to help with a problem if it has lots of replies.
I would go with a substitution first. [EDIT] Whoops, that doesn't work. Let me think about that a bit more.
You have . The derivative of the arctan function is always positive, hence you have a monotone increasing function. Moreover, . From those pieces of information, and the fact that the logarithm function is monotone increasing, I think you can infer that the integral in the numerator is infinite.
The book gives me a solution but it's ambiguous for me, i don't understand much from it
I swear, this is all they give me for the solution why that integral -> inf
Maybe this will help you, because it didn't helped me at all.
Damn, not too familiar with mathematics in english O.o (i don't know the terminology in English)