Maclaurin Series For Tanx Math

From the table below you can notice that sech is not supported but you can still enter it using the identity sech x 1 cosh x.

Maclaurin series for tanx math. The th term of a maclaurin series of a function can be computed in the wolfram language using seriescoefficient f x 0 n and is given by the inverse z transform 2. The first one is easy because tan 0 0. The maclaurin series of a function up to order may be found using series f x 0 n. Partial sums of a maclaurin series provide polynomial approximations for the function.

A maclaurin series can be used to approximate a function find the antiderivative of a complicated function or compute an otherwise uncomputable sum. A maclaurin series is a special case of a taylor series obtained by setting x 0 0 x0. Deriving the maclaurin series for tan x is a very simple process. Let the maclaurin series for tan x be tan x a 1 x a 3 x 3 a 5 x 5.

The first derivative of tan x is very simple as you can see. Ii by using the relationship s e c 2 x 2 tan 2 x. Maclaurin series are named after the scottish mathematician colin maclaurin. If you get an error double check your expression add parentheses and multiplication signs where needed and consult the table below.

It is more of an exercise in differentiating using the chain rule to find the derivatives. As you can imagine each order of derivative gets larger which is great fun to work out.