2. Find the product AB of two matrices.2.[1B-1a) A =L346-121-13. Let A and B be 4 x 5 matrices and let C, D, and E be 5 x 2, 4 x 2, and 5 x 4 matricesrespectively. Determine which of the following matrix expressions are defined. For thosethat are defined, give the size of the resulting matrix.a) ВАb) AC + Dc) AE + B Activity 1. Use zero – through second - order Taylor series expansions toapproximate the functions below fromvalue at x41 =1.O with h = 1. That is, predict the function's1. f(x) = 1+x+ x?2. f(x) = e*SITY DFLet's Analyze.Activity 1. In this activity you are required to answer matrix related problems and applythe fundamental knowledge of solving for matrices.[3-2-2411. Let A = 64 and B = 0475.then find,a) The first row of ABb) The third row of ABc) The second row of ABNCEd) The first column of BAe) The third row of AAf) The third column of AAITASNALINDA670974.

1. The given function is fx=1+x+x2 and xi=0, h=1. Approximate the function by using the second order…

Answered: 2. Find the product AB of two matrices.…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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(part 1 of 4) Find the coefficient of 6 in the Taylor series expansion centered at the origin for the function f(x) = 6+2 sin(x²). 1. coefficient 2. coefficient ofx6 3. 4. 5. coefficient ofx6 = 2 on (-∞, ∞). = 1 coefficient ofx6 = 3 coefficient ofx6 (part 2 of 4) Find a power series representation for the function f(x) = x sin(2x) 1. f(x) = Σ (−1)n-1. n=1 5. f(x) ∞ 2. f(x) = Σ (-1)″-1. n=1 6. f(x) of 6 = −1 -1 -2 1. 2. ∞ 3. f(x) = Σ (−1)″-1. n=1 3. ∞ 4. f(x) = Σ (−1)n-1. n=1 == = 4. = 5. ∞ 1 3 n=1 Σ(-1)-1 22n 2n 1 2n-1 n - 1 Σ (1)n-1. n=1 f(x) = f(x) = Σn=0 f(x) = Σn=0_n! f(x) = Σn=0 (-1)" 2n n! xn+1 2n (-1)" (2n)! (part 3 of 4) Find the Taylor series centered at the origin for the function - 22n-1 (2n-1)! x = x cos(2x). f(x) = En=0 22n f(x) = Σ=0 (2n)! 2n (n − 1)! 1 (2n)! 1 xn (n − 1)! x²n xn xn+1 x²n+1 (-1)" 22n (2n)! x²n+1 x²n 2n x²n xn x²n+1
2d
1. (50) Solve the differential equation (3 – 2)y" – 3xy' – y = 0 by means of a power series about the ordinary point x = 0. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions. If possible, find the general term in each solution.
1. Use zero-through third-order Taylor series expansions to predict (3) for fix)=25x³-6x² + 7x+88 using a base point at x = 1. Compute the true percent relative error &, for each approximation. h = 3-1=2 Record your result on the table. 2.. Use zero-through third-order Taylor series expansions to estimate f(x) = e-* using a base point at x = 1 for x = 0.2. Compute the true percent relative error E, for each approximation. A = 0.8 Record your result on the table. Order 0 1 2 3 Order 0 1 2 3 Value Value E₁ E₁
4
Solve for the value of f(x) = e³xx4 Using 12 term Taylor series if x = 0.056
TT TU 1. Use Taylor Series Expansion to approximate the value of f(x) = sin(x) at x₁+1 = and xi = = Calculate from 0-5 iterations. Show your solution for every iteration and follow the table below for your 3 4 answers. Iteration f(n) (x) (3) approx. Approx. Error
I need help with A and B, thanks
Determine f (-2) and f(4)(–2) for a function with Taylor series T (x) = 3(x + 2) + (x + 2)² – 4(x +2)³ + 2(x + 2)ª + · . .
Let f(x)=e−xf(x)=e−x. We're going to calculate the Taylor series for this function near a=0a=0 . Calculate f(0),f′(0),f′′(0),f(0),f′(0),f″(0), and f(3)(0)f(3)(0) . What patterns do you notice here? Write down the degree 3 Taylor polynomial approximation for f(x)f(x) near a=0a=0 . Make a graph that shows the function and the degree 3 Taylor polynomial. For what interval of x-values is this a relatively good approximation? For which x-values is this not a very good approximation? Based on the patterns you observed in (a), find a general formula for the k-th derivative of this function when evaluated at 0.f(k)(0)=?f(k)(0)=? Write the Taylor series fo f(x)f(x) near a=0a=0, using sigma notation. What is the interval of convergence for this series? What would be different about your result if we instead calculated the Taylor series for f(x)f(x) near a=4a=4 ?
can you clearly show your working, thanks
The coefficient of (x - 2)4 in the Taylor series expansion of f(x) = 3 log x - log x² about x = 2 is x 10-3.

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