so my general function are bigger then their taylor series by the remainder of Rn

the functions are greater than the Taylor polynomial up to power n

by the members which are in a higher powers then "n"

this is the logic

how to formulate it into equation??

i got the idea that its the function is bigger then the polynomial by the members with powers higher then "n".

 

but its only a logic

how to formulate it into mathematical equations??

 

the remainder formula is

0<c<x

[math]

R_n(x)=\frac{f^{n+1}©}{(n+1)!}x^{n+1}

[/math]

 

so i guess that for x>0 its:

[math]

R_n(x)=\frac{f^{n+1}©}{(n+1)!}x^{n+1}

[/math]

 

for x<0

[math]

R_n(x)=-\frac{f^{n+1}©}{(n+1)!}x^{n+1}

[/math]

 

should i prove it by induction??

if so then if n=1 then

[math]

e^x=1+x+ \frac{f^{1+1}©}{(1+1)!}x^{1+1}

[/math]

 

but i dont know whats the value of c??

and still it depends on the values of x

??