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I'm in a tight call now. Been trying to understand my maths for the upcoming exam from now monday, but can't figure out how to do the exercises. Been asking around for help, sent my bro with some examples to ask his math teacher, but no help from anywhere, yet monday's creeping closer and closer, so I'll ask here. Anybody here that can explain me how to solve these types of questions? Some examples... (if some words seem odd, that'd be due to bad translation then)

(a) Prove that the function f : x -> x^5 - x - 1 has exactly one zeropoint in the interval [0,2].
(b) Near this zeropoint with the bisection-method with an error that's smaller than 10^-1.
(c) How many steps are needed to calculate the zeropoint with an error that's smaller than 10^-12?

Be D the area
D = {(x,y) e R^2 | x > 0, y > 0, x + y < 2, x^2 + y^2 > 2}.
(a) Make a sketch from D.
(b) Calculate the integral ?D? 1/(x^2 + y^2)^2 dx dy.

Kon-Tiki wrote: (a) Prove that the function f : x -> x^5 - x - 1 has exactly one zeropoint in the interval [0,2].

The integral changes direction (up/down) exactly once. Not sure if that's of any help...

Thought:
x^5 = x+1

Be D the area
D = {(x,y) e R^2 | x > 0, y > 0, x + y < 2, x^2 + y^2 > 2}.
(a) Make a sketch from D.
(b) Calculate the integral ?D? 1/(x^2 + y^2)^2 dx dy.

Not nice to call it R^2, call it RxR.

See this as a plain graph with X and Y, where you draw an area of all combinations of X and Y, where X > 0 (draw a line there), Y > 0 (line there), x+y<2 (line there) and x^2+y^2 > 2 (line there). Three straight lines, one angled parabole. The first two delimit you to the upper right hand quarter. The other two define an area (between the lines). That's D.

The point of integrating a set (or an area) is completely beyond me.
[edit] no hyperbole [/edit]

Why I'd need to know these's beyond me. Seems like making a quick program to draw it for me's easier... even in QBasic. Anyways, thanks for the quick reply Still will be hard as hell to solve similar questions, but then again, I've never been a math wizz.

w00t! Friend of mine gave me this link. Can continue my studying again

Kon-Tiki wrote: Why I'd need to know these's beyond me. Seems like making a quick program to draw it for me's easier...

And you would draw... which interval? From -100 to +100? Are you sure that would cover any zeropoints?

The idea is that you should be able to write a program that finds the zeropoints without drawing the graph and parsing it again...

(I don't say I'd be able to do it myself. The last five years I've worked in the software industry with blissfully few "encounters" with math...)

Fifth exercise, in the solution, how'd they get -6? I'd say that, logically, the outcome'd be non-existing, due to division by 0...

Edit: Nevermind. Got it