Learn the definition of Maclaurin series and browse a collection of 155 enlightening community discussions around the topic.
The general Maclaurin series formula in summation form looks like this: {eq}f(x)= \sum_{n=0}^{\infty}\dfrac{f^{n}a}{n!}(x-a)^n {/eq}. The {eq}n {/eq} stands for the number of the term (the {eq}n {/eq} value of the first term is 0). The {eq}n! {/eq} is ...
Use a power series to approximate the definite integral to six decimal places: int_0^0.3 x^2 1+x^4 dx. 1. Calculate each value using the Maclaurin series expansion. Then find the calculator value correct to 6 places. a) e^{0.5} b) cos(1.57) c) ln(2.5) 2. Is...
Roughly speaking, the bound (3) would follow from (4) by setting , provided that we can show that the terms of the left-hand side dominate the sum in this regime. This can be done, after a technical step of passing to tuples which nearly optimize the required inequality (3). We ...