Taylor polynomial

A Taylor polynomial is a partial Taylor series that helps approximates the function $f(x)$ near $x=a$. The more term the polynomial have, the lesser the magnitude of error. $P(x)=f(a)+f^{\prime }(a)(x-a)+\frac{f^{\prime \prime }(a)}{2!}(x-a{)}^2+\frac{f^{(3)}(a)}{3!}(x-a{)}^3+\cdots$