Αποτελέσματα Αναζήτησης
The Remainder theorem tells: For every x on [c−d,c+ d] the error term satisfies the bound |f(x) −P n(x)|≤M (n+1) (x−c)n+1 (n+ 1)! Example: For f(x) = ex and c = 0 we have R n(x) = ex (x−0)n+1 (n+ 1)!. For x = 1, this gives the bound R n(1) = e/(n + 1)! which for n = 5is R 5(1) = e/720 = 0.00377. The actual error is e −(1 + 1 + 1/2 ...
use of generalized functions related to the Dirac "delta function" in the typical way suitable for applications in physics and engineering, without adopting the language of distributions.
(a) Find the remainder when f(x) is divided by (x + 2). (2) (b) Use the factor theorem to show that (x + 3) is a factor of f(x). (2) (c) Factorise f(x) completely. (4) (Total 8 marks) 10. f(x) = 2x3 – x2 + ax + b, where a and b are constants. It is given that (x – 2) is a factor of f(x). When f(x) is divided by (x + 1), the remainder is 6.
analysis, then covers Gamma and Elliptic functions in some de-tail, before turning to the main theme of the course: the unified study of the most ubiquitous scalar partial differential equations of physics, namely the wave, diffusion, Laplace, Poisson, and Schrödinger equations. I show how the same mathematical me-
Motion in one dimension (1D) In this chapter, we study speed, velocity, and acceleration for motion in one-dimension. One dimensional motion is motion along a straight line, like the motion of a glider on an airtrack.
Definition: A relation ∼ on a set X is an equivalence relation if for every a, b, c ∈ X, a ∼ a. if a ∼ b then b ∼ a. if a ∼ b and b ∼ c then a ∼ c. Definition: Under and equivalence relation ∼ on the set X, the equivalence class of x ∈ X is [x] = {y ∈ X | x ∼ y} the set of all equivalent elements. .1. if.
In this section you will learn to: understand the definition of a zero of a polynomial function. use long and synthetic division to divide polynomials. use the remainder theorem. use the factor theorem. Example 1: Use long division to find the quotient and the remainder: Steps for Long Division: 5593 ÷ 27.
