Hi mathlovers ,

Obtain a function whose first difference is $ e^x $. Can any member give me hint to solve this problem?

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- Mar 4th 2014, 05:29 AMVinodProblem in finite differences
Hi mathlovers ,

Obtain a function whose first difference is $ e^x $. Can any member give me hint to solve this problem? - Mar 4th 2014, 06:21 AMPlatoRe: Problem in finite differences
- Mar 4th 2014, 06:59 AMVinodRe: Problem in finite differences
- Mar 4th 2014, 07:42 AMPlatoRe: Problem in finite differences
- Mar 5th 2014, 01:14 AMBobPRe: Problem in finite differences
Call your values

and the corresponding function values

then the entries in the first difference column will be

.

If you were to divide each of these by you would get a discrete version of the derivative of

If this is to be/represent what does that suggest that should be ? Think calculus.

Make that (obvious) choice for and construct the first difference column, (a little algebraic simplification is required).

You should find that that doesn't quite work, but after tweaking slightly it does. - Mar 5th 2014, 04:33 AMVinodRe: Problem in finite differences
Hi,

I got the answer to the problem by referring to the solved answers to the similar finite differences problems. Here is the answer. We have $ e^x $ as first difference

$ e^x =e^x\frac {1-e}{1-e} $

$ e^x =\frac {e^x}{1-e}-\frac {e^{x+1}}{1-e} $

Hence,

the function is$\frac {e^{x+1}}{1-e} $ - Mar 5th 2014, 05:11 AMBobPRe: Problem in finite differences
Why rather than ?

Doesn't your choice produce in the first difference column ?

Also, you assume a step length of 1, does that have to be the case ? - Mar 5th 2014, 05:29 AMVinodRe: Problem in finite differences