Series

The Maclaurin series expansion of ex or the Taylor series expansion of ex at x=0 is given by the following summation: ex = $\sum _{n=0}^{\mathrm{\infty }}{\displaystyle \frac{x^n}{n!}}$ = $1+x+{\displaystyle \frac{x^2}{2!}}+{\displaystyle \frac{x^3}{3!}}+{\displaystyle \frac{x^4}{4!}}+\cdots$. In this post, we will learn how to find the series expansion of ex. Taylor Series Expansion of ex at x=0 The Maclaurin series expansion of a function … Read more

The Maclaurin series expansion of cosx or the Taylor series expansion of cosx at x=0 is given as follows: cosx = $\sum _{n=0}^{\mathrm{\infty }}{\displaystyle \frac{(-1{)}^n}{(2n)!}}{x}^{2n}$ = $1-{\displaystyle \frac{x^2}{2!}}+{\displaystyle \frac{x^4}{4!}}-{\displaystyle \frac{x^6}{6!}}+\cdots$ Taylor Series Expansion of Sinx at x=0 Note that the Maclaurin series expansion of f(x)=cosx or the Taylor series of a function f(x) at $x=0$ is given by the following … Read more

The Maclaurin series expansion of sinx or the Taylor series expansion of sinx at x=0 is given as follows: $\sin x=\sum _{n=0}^{\mathrm{\infty }}{\displaystyle \frac{(-1{)}^n}{(2n+1)!}}{x}^{2n+1}$ $=x-{\displaystyle \frac{x^3}{3!}}+{\displaystyle \frac{x^5}{5!}}-\cdots$ Taylor Series Expansion of Sinx at x=0 We know that the Maclaurin series expansion of $\sin x$ or the Taylor series of a function $f(x)$ at $x=0$ is given by the … Read more