GeoGebra: The Binomial Expansion
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Fully interactive: A geometric representation of the binomial expansion
Control parameters a,b,n in the function f(x)=(a+bx)n
Also control the number of terms in the binomial expansion.
The applet shows the correct function (black) alongside the binomial expansion of the function (green).
It also clearly shows the bounds (x-values) for which the expansion is valid.
Note that the validity bounds are independent of the number of terms in the expansion.
i.e. an expansion may be ‘valid’ for a particular value of x, but this does not necessarily mean the approximation is good; you may need more terms in the expansion.