f(x)= 3+ 1/27 x- 1/2 187 x^2+5/53 144 1 x^3+o(x^3)

∴f(30)=3+ 1/27×(30-27)- 1/2 187×(30-27)^2+5/53 144 1×(30-27)^3≈3. 1072

That is 30 (1/3) ≈ 3. 1072.

Taylor formula is a formula that uses the information of a function at a certain point to describe its nearby value. If the function meets certain conditions, Taylor formula can use the derivative values of each order of the function at a certain point as coefficients to construct a polynomial to approximate the function. Taylor formula is named after British mathematician Brook Taylor, who first described it in a letter 17 12. Taylor formula is one of the commonly used approximate methods to study the properties of complex functions, and it is also an important application content of function differential calculus.

Brook Taylor, a mathematician, was one of the most outstanding representatives of the British Newton School in the early18th century. His main work was The Method of Positive and Negative Increments published in 17 15, in which he stated the famous theorem-Taylor in a letter to his teacher Meiqin in July12.

17 17 Taylor uses Taylor's definition to understand numerical equations. Taylor formula is developed from Gregory-Newton difference formula, which uses the information of a function at a certain point to describe the value near it. If the function is smooth enough, Taylor formula can construct a polynomial to approximate the function value in the neighborhood of the point with these derivative values as coefficients on the premise of knowing the derivatives of each order.