00:01
Hello everyone, so this is the question that we have.
00:03
We need to compare the numerical differentiation formula for the central difference.
00:11
Central difference of the function f of x is equal to 0 .104 x cube, 0 .104 x whole cube using the taylor series and find the approximations for f dash of 2.
00:31
First of all, we need to use the central difference.
00:35
O .h2 with formula, h is equal to 0 .05, and similarly is oh4fid, h is equal to 0 .05 again.
00:46
Now let's jump on to the solution of the question.
00:49
So how do we give the taylor approximation? the taylor series is given by, say, fx plus h.
01:00
It will be given by f of x plus h.
01:03
Divided by 1 factorial multiplied by f dash of x plus h squared divided by 2 factorial f double dash of x plus h cube of 3 factorial f triple dash of x and so on and so forth similarly if i have f of x minus h it would be given by f of x minus x minus x minus h divided by one factorial f dash of x.
01:40
Now negative is come, positive now, is squared divided by two factorialial, f double dash of x...