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Generate a Taylor series expansion of cos(x) using x, expanding about x = 0 and
continuing until a term with x^6. Taylor series about x = 0 are called Maclaurin
series.
(*
* Generate a Taylor series expansion of cos(x) using x, expanding about x = 0 and
* continuing until a term with x^6. Taylor series about x = 0 are called Maclaurin
* series.
*)
Series[Cos[x], {x, 0, 6}]
1 - x^2/2 + x^4/24 - x^6/720 + O[x]^7
The 'O[x]^7' just represents the rest of the series, which we don't care about.
If you don't want it displayed, just wrap the call to Series inside a call to
Normal: Normal[Series[...]]. This is useful for plotting series.
Here's the same function, but expanded about a different point, x = 3pi/2:
(*
* The 'O[x]^7' just represents the rest of the series, which we don't care about.
* If you don't want it displayed, just wrap the call to Series inside a call to
* Normal: Normal[Series[...]]. This is useful for plotting series.
*
* Here's the same function, but expanded about a different point, x = 3pi/2:
*)
Series[Cos[x], {x, 3 Pi/2, 6}]
(x-3pi/2) - 1/6*(x-3pi/2)^3 + 1/120*(x-3pi/2)^5 + O[x-3pi/2]^7
When plotting series, remember to wrap the function in both a call to Normal AND
a call to Evaluate: this strips the extra term mentioned previously and tells
Mathematica to actually evaluate the function rather than hold it as an expression.
(*
* When plotting series, remember to wrap the function in both a call to Normal AND
* a call to Evaluate: this strips the extra term mentioned previously and tells
* Mathematica to actually evaluate the function rather than hold it as an expression.
*)
Plot[Evaluate[Normal[Series[Cos[x], {x, 0, 6}]]], {x, 0, 1}]