isfunction = true or false

Whether to find the rate of convergence of a sequence or a function.  If S is a function, isfunction must be set to true. By default, isfunction=false.

If the input is a sequence $a^n$, the return value of the RateOfConvergence command is of the form $L+\mathrm{O}\left(n^{-d}\right)$, where $L=\underset{n\to \mathrm{\infty }}{lim}{a}_n$ and $a_n-L=\mathrm{O}\left(n^{-d}\right)$ for some $0<d$.

If the input is a function $f\left(x\right)$, the return value is of the form $L+\mathrm{O}\left(x^d\right)$, where $L=\underset{x\to 0}{lim}f\left(x\right)$ and $f\left(x\right)-L=\mathrm{O}\left(x^d\right)$ for some $0<d$

If S is a function, the option isfunction must be set to true.

By default, the isfunction option is set to false.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{NumericalAnalysis}\right]\right)\&colon;$

$\mathrm{RateOfConvergence}\left(1+\frac{1}{n}\&comma;n\right)$

$1+\mathrm{O}\left(\frac{1}{n}\right)$

$\mathrm{RateOfConvergence}\left(\frac{1}{2}-\frac{1}{n^2}\&comma;n\right)$

$\frac{1}{2}+\mathrm{O}\left(\frac{1}{n^2}\right)$

$\mathrm{RateOfConvergence}\left(\exp \left(x\right)\&comma;x\&comma;\mathrm{isfunction}=\mathrm{true}\right)$

$1+\mathrm{O}\left(x\right)$