I don't need to "derive this formula", i already know how to do it$.$

I just want to know how to "Find the leading error term of above formula and discuss the results."

And i just want to know that the relations between $\backslash$kappa $^(*)\backslash$Delta x vs$.\backslash$kappa $\backslash$Delta x

$($a$)$ Derive a sixth$-$order compact $($or Pad$)$ finite$-$difference approximation to a first derivative in the form

$\backslash$alpha $($u$\_($x$))\_($i$-1)+($u$\_($x$))\_($i$)+\backslash$beta $($u$\_($x$))\_($i$+1)=$au$\_($i$-2)+$bu$\_($i$-1)+$cu$\_($i$)+$du$\_($i$+1)+$eu$\_($i$+2).$

Find the leading error term of above formula and discuss the results.

$($b$)$ Find the modified wavenumber for the above operator. Plot the real and imaginary parts of $\backslash$kappa $^(*)\backslash$Delta x vs$.$

$\backslash$kappa $\backslash$Delta x for kappa $\backslash$Delta xpi $.$