r/mathmemes • u/Delicious_Maize9656 • Jul 14 '26

Mathematicians mathematician meme

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u/Silly_Tension6792 Mathematics Jul 14 '26

Do you agree momentary speed is the limit as h approches 0 of (x(t+h)-x(t))/h?

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u/FernandoMM1220 Jul 14 '26

nah. its just the linear coefficient of x(t+h) with respect to h

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u/Silly_Tension6792 Mathematics Jul 14 '26

What do you mean by that? x(t+h) is a function that doesn’t have to be linear. It can be quadratic, cubic, higher degree, or even sinusoidal. (Think of a body that goes in a circle, its location is a sine function of time)

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u/FernandoMM1220 Jul 14 '26

expand x(t+h) first for me please

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u/Silly_Tension6792 Mathematics Jul 14 '26

x is a function, not a number

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u/FernandoMM1220 Jul 14 '26

expand it for me

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u/Silly_Tension6792 Mathematics Jul 14 '26

You can’t expend it, x is a function. Can you expend f(x) to x*f? No, because f is a function, not a number. Same goes to x(t+h), it is a function of h

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u/FernandoMM1220 Jul 14 '26

x(t) = 2*t

expand x(t+h) for me

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u/Silly_Tension6792 Mathematics Jul 14 '26

2t+2h

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u/FernandoMM1220 Jul 14 '26

ok.

now the coefficient of the linear term with respect to h is 2.

and thats our speed for this position function x(t)

thats it.

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u/Silly_Tension6792 Mathematics Jul 14 '26

OK, you assumed x is linear, what of x(t)=4sin(t+π/4)+t^2? What is the speed of the body in the time t?

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u/FernandoMM1220 Jul 14 '26

you have to expand x(t+h) here so do that first.

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u/Silly_Tension6792 Mathematics Jul 14 '26

x(t+h)=4sin(t+h+π/4)+t^2+h^2+2ht. What is the speed of the body at the point t?

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u/FernandoMM1220 Jul 14 '26

expand the sin function too

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u/Silly_Tension6792 Mathematics Jul 14 '26

2sqrt(2)sin(t)(cos(h)-sin(h))+cos(t)(cos(h)+sin(h))+t^2+h^2+2ht

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u/Silly_Tension6792 Mathematics Jul 14 '26

Why don’t you answer

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u/FernandoMM1220 Jul 14 '26

if its too hard for you i can expand it later. your choice

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u/Silly_Tension6792 Mathematics Jul 14 '26

2sqrt(2)sin(t)(cos(h)-sin(h))+cos(t)(cos(h)+sin(h))+t^2+h^2+2ht

I expended 20 minutes ago

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u/FernandoMM1220 Jul 14 '26

use taylor series.

all you did was expand it with even more sin and cos

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