Question

Which of the following statements are true? Statement A: A Taylor Series is a polynomial used to approximate other functions. Statement B: Lower degree Taylor Polynomials provide better approximations about a centre. Neither Anor B B only Both A and B O A only

Answer 1

A Taylor Series is a polynomial used to approximate other functions. Lower degree Taylor Polynomials provide better approximations about a center. The correct statements are Option A only.

Step-by-step explanation:

Statement A: A Taylor Series is a polynomial used to approximate other functions. This statement is true. A Taylor Series is an expansion of a function into an infinite sum of terms, where each term is a derivative of the function evaluated at a specific point. The Taylor Series can be used to approximate functions by considering only a finite number of terms in the series.

Statement B: Lower degree Taylor Polynomials provide better approximations about a center. This statement is false. Higher degree Taylor Polynomials provide better approximations about a center. As the degree of the polynomial increases, the approximation becomes more accurate. Lower degree Taylor Polynomials provide less accurate approximations.

Therefore, the correct answer is Option A only.