Taylor Polynomial Calculator

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Taylor polynomial calculator is used to calculate functional sum of a Taylor series. Taylor series is a function of infinite sum of situations, calculated from its derivative’s values about a point. Taylor polynomial is given by:

P_n(x)= f(a)+(x-a)f’(a) / 1! + (x -a)² f’’(a) / 2! + ……(x+a)ⁿfⁿ(a)/n!

Example 1: Explain what is Maciaurin polynomial.

Taylor series in which for a function y =f(x) by a polynomial near x=a of degree n. This means that the function y= f(x) in which

the upper value for x is a and number of degree or values will be n will be given by

P_n(x) = a₀ + a₁(x-a) + a₂(x-a)² + …… a_n(x-a)ⁿ

When a = 1, then this taylor polynomial is known as Maciaurin polynomial.

Example 2: Explain what is second degree Taylor ploynomial

We use quadratic polynomial to approximate that function. Also polynomial that has same value as the function has at any

point like a. This has same derivative at point a and same second derivative at that point.

$f(x)\approx P_{_}{2}(x) = f(a)+ f’(a) (x-a) + \frac{f’(a)}{2} (x-a)^{2}$

We see that the 1^st and 2^nd derivative of P2(x) is same as the function f(x) does at the point x = a.

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