ds-dt-v-dv-dt-a-da-dt-b-db-dt-e-de-dt-f-df-dt-g-dg-dt-h-dh-dt-i-di-dt-j-dj-dt-k-now-if-we-continue-this-process-to-infinity-and-if-v-0-v-a-b-e-f-g-h-i-j-1

Question Number 13751 by Nayon last updated on 23/May/17

\frac{d s}{d t} = v, \frac{d v}{d t} = a, \frac{d a}{d t} = b, \frac{d b}{d t} = e, \frac{d e}{d t} = f

\frac{d f}{d t} = g, \frac{d g}{d t} = h, \frac{d h}{d t} = i, \frac{d i}{d t} = j, \frac{d j}{d t} = k, \dots . .

n o w i f w e c o n t i n u e t h i s p r o c e s s t o

i n f i n i t y . . a n d i f v_{0}, v, a, b, e, f, g, h, i,

j, \dots \dots \dots \dots \dots . = 1 . t h e n c a l c u l a t e

t h e f o r m u l a o f v a n d s \dots

Commented by ajfour last updated on 23/May/17

s = v = e^{t}

Commented by Nayon last updated on 23/May/17

d e t A i l s

Commented by Nayon last updated on 23/May/17

v = e^{t} r i g h t b u t

s = e^{t} - 1

Commented by ajfour last updated on 23/May/17

a g r e e

Answered by ajfour last updated on 23/May/17

s (t) = s (0) + {t s}^{'} (0) + \frac{t^{2}}{2!} s^{″} (0) + \dots

a n d i n q u e s t i o n,

s^{'} (0) = s^{″} (0) = \dots . = 1, s (0) = 0

s o, s (t) = - 1 + (1 + t + \frac{t^{2}}{2!} + \dots .)

s (t) = e^{t} - 1

v (t) = \frac{d s}{d t} = e^{t} .

Commented by Nayon last updated on 24/May/17

H a s t h e r e a n y o b j e c t i n t h e

u n i v e r s e w h i c h a d h e r e t h i s f o r m u l a ?

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