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## Main Question or Discussion Point

i have few doubts about differential equations and numerical methods ...

in a differential equation question ... you are given an instantaneous rate of change...

and you are supposed to find the function that gives , this instantaneous rate of change

is this same as ...

f(0)=1,

f(0.01)=1.01,

f(0.02)=1.0201,

f(0.03)= 1.030301

??

in a differential equation question ... you are given an instantaneous rate of change...

and you are supposed to find the function that gives , this instantaneous rate of change

Numerical methods approximate the "instantaneous rate of change" with "the rate of change over a small interval".

is this same as ...

f(0)=1,

f(0.01)=1.01,

f(0.02)=1.0201,

f(0.03)= 1.030301

??