Taylor Series Non Zero Term Calculator

Taylor Series is a fundamental concept in calculus, used to approximate functions using polynomials. The non-zero term calculator helps you find the nth non-zero term in the Taylor Series expansion of a given function at a specific point.

1. Select the function (sin(x), cos(x), or tan(x))
2. Enter the value of x
3. Enter the value of n
4. Click ‘Calculate’

The nth non-zero term in the Taylor Series of a function f(x) at a point a is given by:

Tn(x) = f^(n)(a) / n! * (x - a)^n

where f^(n)(a) is the nth derivative of f(x) evaluated at x = a.

Comparison of Taylor Series approximations for sin(x) at x = π/4

n	Taylor Series Approximation	Actual Value

• Taylor Series converges to the function for most functions at points where the function is well-behaved.
• For some functions, the series may converge to a different value (convergence to a different function).
• Taylor Series can be used to approximate derivatives and integrals.

What is the Taylor Series?

The Taylor Series is a representation of a function as an infinite sum of terms that are calculated from the values of the function’s derivatives at a single point.

For more information, see the following authoritative sources:

• Maths is Fun – Taylor Series
• Khan Academy – Taylor Series