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f(w,t)=sin(wt)/w. Help make defined at w = 0. (discuss.tchncs.de)
submitted 1 month ago* by to c/math@lemmy.world
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Is there a way to make the function

f(w,t)=sin(wt)/w

defined at w = 0?

I want to achieve better numerical stability, and make it continuous everywhere.

Observation: Using limw->0 f(w,t)

I know that at w = 0:

f(0,t) = t

Is it possible to improve this function? I would be really glad to know and why, how. Thank you in advance!

I really do not want to code in smth like: if w < 0.001 { x = t; }

Background notes: My equation also has constant v coefficient, but I removed it for simplicity. f(w,t)=v*sin(wt)/w

If I derived this correctly this should be x component of a motion of a car that rotates with rate w. It goes with const speed and const steer.

These are consts: v - speed, l - base length(dist from rear to front shaft), a - steering angle.

w(a) is defined idk if correctly. w(a) = (vsin(2a))/(2*l) I just logically added proportions, projections, imagining a rear wheel powered car. Put some values I am somewhat confident in, such as: w(0) = 0 w(π/2) = 0

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[–] 1 point 1 month ago* (last edited 1 month ago)

If you'd put anywhere near as much thought and effort into the mathematics as you did into gatekeeping learning, you'd see that there's a genuine issue approaching zero from different directions in this function RxR->R and it's not obvious what to do about that.

This is not stackoverflow. Stackoverflow was dying before LLMs, and it's this kind of critical and/or hostilenon-answering response to beginners' questions that killed it.

You can't be bothered to think about or answer the question, and somehow you've concluded that the student who has actually done some work on the project is the lazy one who needs to be belittled.

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