Find the binomial expansion for the power (n-1) and the differentiate the given equation in question.
By differentiating each side of (1 + x)" = 22=0 (3).x* and comparing the coefficients of...
23 If - 3 22 - 3 is equal 1, what is the solution for x? {0} No Solution All real numbers, except x + Ž {}
Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series. 1 using fix) 2 g(x)= (1+4x2)2 gix)-ΣΠ k 0 The power series g(x) converges on the interval (Simplify your answer. Type your answer interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) Find the power series representation...
please solve Q1 and Q2 3 ths Homework - Rate My Maths Homework - X Differentiating parametrics k/differentiating parametric functions 10 Q2 - Tangents and normals A curve is defined parametrically as 12 Q2 + x= 1, y = 13 Find dy dx at the point 1 = 3. dy dx 10 Computer and Mathematical Sciences Find the gradient of the tangent to the curve 1 Find the equation of the tangent to the graph at t = 3. at...
Just part e plz e) Compute the complex Fourier coefficients for 0(2) =-22, x E [-π, π]. f) Consider the PDE Ση-| aijUziz,(x)-0. Determine the type of the P e) Compute the complex Fourier coefficients for 0(2) =-22, x E [-π, π]. f) Consider the PDE Ση-| aijUziz,(x)-0. Determine the type of the P
4. Define the function f(x) = x/(e* – 1) so that f(0) = 1, then the Maclaurin expansion of f(x) has a positive radius of convergence. a) When the Maclaurin expansion is expressed in the form B2 B3 3 i=1+ B13 +31 x2 + x3 + ... + x" + ... n! the coefficients B1, B2, B3,... are called the Bernoulli numbers. Substitute the Maclaurin series for et and use polynomial long-division to find the first four Bernoulli numbers. b)...
7.3 Practice Problems Prove each of the following statements using mathematical induction. 1. Show that 2 + 4 +8+ ... +2n = 20+1 -2 for all natural numbers n = 1,2,3,... y lo 2. Show that 12 +22+32 + ... + n2 = n(n+1)(2+1) for all natural numbers n = 1,2,3,...
3. Let X X be a random sample from Uniform[0, where > 0 is unknown. (a) Show that = max{X,X is the MLE of 0. (b) Let the CDF of @ be F(-). Find F(t) for any t e R (c) Find the pdf of 0 Hint: Find the distribution function of Z maxX1,X. The first feu steps will be as follous: F2(2) P(Z) P (maxX, x) ) = P (XS2, X X,) Nert use the fact that Xis are...
Find the indicated coefficients of the power series solution about x=0 of the differential equation. (x^2+1)y''-xy'+y=0, y(0)=3, y'(0)=-6 (1 point) Find the indicated coefficients of the power series solution about 0 of the differential equation (x2 1)y ry y 0, (0) 3, y' (0) -6 r2 24+ r(9) (1 point) Find the indicated coefficients of the power series solution about 0 of the differential equation (x2 1)y ry y 0, (0) 3, y' (0) -6 r2 24+ r(9)
Section A Q1 0 Using the following Taylor series expansion: f(x+h) = f(x)+hf'(x)+22 h 3! f"(x)+ (+0) (1.1) 4! show that the central finite difference formula for the first derivative can be written as: f'(x)= f(x+h)-f(x-1) + ch" +0(hº) (1.2) 2h Determine cp and of the derived equation. [4 marks] Consider the function: f(x) = sin +COS (1.3) 2 2 Let x =ih with n=0.25, give your answer in 3 decimals for (ii) to (vi): (ii) Evaluate f(x) for i...
3. (a) Given n e N, prove that sup{.22 : 0<x<1} = 1 and inf{.22n: 0<x<1} = 0. (b) Find the supremum of the set S = {Sn: ,ne N}. Give a proof.