What is the Taylor series expansion for COS X?

Taylor series expansion of f=cos(x) about x=0. Problem 4.10 asks us to increment n from 1 until the approximate error indicates that we have accuracy to two significant digits for x=pi/3.

What is series expansion Mathematica?

Power series are in many ways the algebraic analog of limited-precision numbers. The Wolfram Language can generate series approximations to virtually any combination of built-in mathematical functions. It will then automatically combine series, truncating to the correct order.

What is the inverse of cosine?

The arccos function is the inverse of the cosine function. It returns the angle whose cosine is a given number. Means: The angle whose cosine is 0.866 is 30 degrees. Use arccos when you know the cosine of an angle and want to know the actual angle.

What is the expansion of sin2x?

2sin2x+sin22x=2.

What is the Maclaurin series for e x?

So the Maclaurin series is: ex=1+1×0!

How do you calculate ex expansion?

the expansion of e^(x) is, e^(x) = 1+x+x^2/2!

How do you find the series expansion of the inverse trigonometric functions?

Since Sec (x), Csc (x) and Cot (x) are reciprocal of Cos (x), Sin (x) and Tan (x) respectively, the expansion of them are easily obtained by replacing x by 1/x. Thus we see that the series expansion of the inverse trigonometric functions can be obtained easily using mere integration without doing the cumbersome Taylor expansion.

How do you find the inverse of Tan in series expansion?

Let us first consider the inverse of Tan (x) which has the simplest form of series expansion. Our first step is to find the derivative of ArcTan (x), which is 1/ (1+x^2). Since integration is the inverse operation of derivative, ArcTan (x) will be same as the integral of 1/ (1+x^2).

What is a series expansion in math?

Series Expansion A series expansion is a representation of a particular function as a sum of powers in one of its variables, or by a sum of powers of another (usually elementary) function. Here are series expansions (some Maclaurin, some Laurent, and some Puiseux) for a number of common functions. (1)

Is the radius of convergence of cos x the same as sin x?

The theorem mentioned above tells us that, because the radius of convergence of cos (x) will be the same as sin (x). However, we haven’t introduced that theorem in this module. You may want to ask your instructor if you are expected to know this theorem.