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3 dni temu · Find the value of $A$ where $$A=\sum_{n=1}^{\infty}\left(n\sin\left(\frac{\pi n}{2}\right)\left(e^x-1-\frac{x}{1!}-\frac{x^2}{2!}-\cdots-\frac{x^n}{n!}\right)\right)$$ By using the expansion of $e^x$ , I have simplified the expression into $$A=\sum_{n=1}^{\infty}\left(n\sin\left(\frac{\pi n}{2}\right)\left(\sum_{i=n+1}^{\infty}\frac{x^i}{i ...
3 dni temu · This modulo calculator is a handy tool if you need to find the result of modulo operations. All you have to do is input the initial number x and integer y to find the modulo number r, according to x mod y = r. Read on to discover what modulo operations and modulo congruence are, how to calculate modulo and how to use this calculator correctly.
4 dni temu · L'Hôpital's rule. Example application of l'Hôpital's rule to f(x) = sin (x) and g(x) = −0.5x: the function h(x) = f(x)/g(x) is undefined at x = 0, but can be completed to a continuous function on all of R by defining h(0) = f′ (0)/g′ (0) = −2. Part of a series of articles about.
13 godz. temu · Automatic differentiation. In mathematics and computer algebra, automatic differentiation ( auto-differentiation, autodiff, or AD ), also called algorithmic differentiation, computational differentiation, [1] [2] is a set of techniques to evaluate the partial derivative of a function specified by a computer program.
5 dni temu · Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology ... Cauchy Principal Value. About MathWorld; MathWorld Classroom; Contribute; MathWorld Book; wolfram.com; 13,196 Entries; Last Updated: Mon ...
5 dni temu · Find the limit. \lim_ {x \rightarrow 0} \frac {\sec x - 1} {x^2}. x→0lim x2secx−1. In this limit, direct substitution gives the indeterminate form \frac {0} {0} 00. We multiply both the numerator and denominator by the conjugate \sec x + 1 secx +1 of the numerator. This gives.
3 dni temu · An illustration of Newton's method. In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function.The most basic version starts with a real-valued function f, its derivative f ′, and an initial guess ...
