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/sci/ - Science & Math

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973985 No.973985 [Reply] [Original]

how do i show that a specific function has exactly one zero?
In my case the function is sin(x)+2x-2.
i can show that the zeroes have to be in [0.5, 1.5], and by naming the only zero i can show that there is one. but how the heck do i show that there is no other in that interval?

pic unrelated, but fun

>> No.974067

The derivative is cos(x) + 2, which is always positive.

If there was more than 1 root, then the secant of those two points would have a slope of 0. Therefore, there has to be at least one point between them where the derivative is 0 (see mean value theorem). Since the derivative is always greater than 0, there can't be two roots.

>> No.974079

The universe has made atoms the size of stars. They're called neutron stars, they're basically gigantic atomic nuclei.

>> No.974095

Show that the function is strictly monotonic in the two intervals.

>> No.974103

What is that in OP's image?

>> No.974105

>>974067
What about when cos(x) = -2? lrn2entirefunction

>> No.974122

>>974105

you mad

>> No.974123

>>974105
cos(x) is between -1 and +1, fag.

>> No.974125

>>974122
NO, U?

>> No.974136
File: 2.79 MB, 515x448, KILLER JELLYFISH.gif [View same] [iqdb] [saucenao] [google]
974136

>>974103
It's a powder toy nuke blowing up a foxy that I made. I've found various ways of destroying my fox stamp.

>> No.974141

>>974123
Reality begs to differ.
http://www.wolframalpha.com/input/?i=acos(-2)

There's actually an infinite number of solutions to cos(x)=-2 but wolfram only displayed the principle one.

>> No.974154

>>974136
>blah blah I MADE THIS. I MADE IT GUISE! ITS MINE blah blah

>> No.974160

God damnit, I want a powder toy thread

>> No.974181
File: 952 KB, 522x257, Action potential.gif [View same] [iqdb] [saucenao] [google]
974181

>>974154
If I implied that, I didn't mean to.
All of my powder toy "art" is open source, or whatever.
It's certainly not bragging (you should have seen the things other people were doing; I'd brag about <span class="math">those[/spoiler])

(Seriously though, powder toy is fun and can be used to model more useful things).

>> No.974192

>>974136
i liek your fox

>> No.974197

>>974181
why do you kill foxxy though :'(

>> No.974201

>>974067
thanks :]

>> No.974211
File: 393 KB, 781x503, temp.png [View same] [iqdb] [saucenao] [google]
974211

>>974197
Wooden fox is made of wood.
I <3 IRL foxes.

>> No.974254

>>974211
fucking furrys

>> No.974283
File: 113 KB, 500x425, Coyote on Bus.jpg [View same] [iqdb] [saucenao] [google]
974283

>>974254
SEE
>>973395
and everything related to it in that thread I accidentally derailed (opps).

(sage because OP's question appears to have been answered)

>> No.974313

>>974141
>>974141
If unspecified in an open forum, one should assume that a speaker means in the set of all real numbers, not in the set of all complex numbers.