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/sci/ - Science & Math

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9685431 No.9685431 [Reply] [Original]

If you take a function f(x)=sinx and take its derivative an infinite amount of times what function do you get back?

And please don't say you have a 1 in 4 chance of getting +/- sin(x)/cos(x)

>> No.9685434

>>9685431
50/50 either it's sin or it's cos
>bounded sequences converge

>> No.9685437

>>9685431
Also if you take that same function f(x) and integrate it an infinite amount of times would you get that same function back?

>> No.9685442

>>9685437
I mean would the infinite integral of sin(x) be the same as the infinite derivative on sin(x) (ignoring c)

>>9685434
See this is what I feel like it should be but I know weird things happen when you take things off to infinity.

>> No.9685445

Is it possible to find a function that is f(x)=tanx with its derivative with respect to x taken an infinite amount of times?

>> No.9685565

>>9685431
50/50 it either happens or it doesn't

>> No.9685584

>>9685431
Retarded question, OP.
To answer you would need to divide infinity by 4 and look at the remainder which is not defined.

>> No.9685817

>>9685431
If you differentiate the function an infinite amount of times how do you measure the end result???????????

>> No.9685818

Infinity should be banned. That's it!!!!

>> No.9685821

[math] \mathscr{Im}( i ^ n \exp(ix)) [/math], where n = infinity

>> No.9686249

Bump

>> No.9686431

>>9685431
Does not exist for all real x

>> No.9687865

You get -1/12

>> No.9687875

>>9685442
Usually how we handle infinity in cases like these is by limits. For sequences of functions (f_n) where f_n : A -> R, it seems natural to define the limit as the unique function f for which, for any epsilon > 0, there exists a natural N so that |f_n - f| < epsilon everywhere in A.

Under this definition, the limit of the sequence of derivatives of sin(x) doesn't exist on any non-degenerate interval (i.e., a point).

Contrast this to the limit of derivatives of e^x, which is e^x. Or any polynomial, which is 0.

>>9685442

>> No.9687911

>>9685431
>If you take a function f(x)=sinx and take its derivative an infinite amount of times what function do you get back?
You can actually study function convergence like this, the function and all its derivatives are an element from L^infinity.

The answer is the sequence doesn't converge, much like the sequence 1,0,1,0,1,0,... does not converge.

>> No.9687921

>>9687911
Your post doesnt clarify anything any non brainlet already knew besides your need to massage your own ego.

>> No.9687926

>>9687921
>any non brainlet
Are you suggesting OP is anything else?

>> No.9688311

Is this a Chinese butcher shop?