The Taylor expansion is one of the most useful ideas in mathematics. Most functions and polynomials are generally smooth to solve. Polynomials are easier to work than almost any other sort of function, and polynomials are largely able to approximate to functions. The Taylor formula gives us an equation for the polynomial expansion for nearly every smooth function of f. Taylor Series In mathematics, the Taylor series of a function is an infinite sum of terms that are expressed in terms of the function’s derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor’s series are…