4. Define the function f(x) = x/(e* – 1) so that f(0) = 1, then the...
A function is defined over (0,6) by 0 <and I <3 f(1) = - { 3<; and <6 We then extend it to an odd periodic function of period 12 and its graph is displayed below. N y 1 0 -10 5 5 10 15 X The function may be approximated by the Fourier series f (t) = a0 + 1 (an cos (021 ) + bn sin ( 122 )), where L is the half-period of the function. Use...
function is defined over (0,6) by f(x)={14x00<xandx≤33<xandx<6. We then extend it to an odd periodic function of period 12 and its graph is displayed below. calculate b1,b2,b3,b4, Thanks so much A function is defined over (0,6) by 0<x and x <3 f (x) = 3<x and x < 6 We then extend it to an odd periodic function of period 12 and its graph is displayed below. 1.5 1 у 0.5 -10 5 10. 15 -1 -1.5 The function may be...
Define a substitution box, So as following table 1 0 3 2 3 2 1 0 0 2 1 3 1 1 3 2 and a substitution scheme that if we denote a 4 bit number as “b1 b2 b3 b4”, the (b1 b4) forms a 2 bit binary number that specifies a row of the above matrix and the (b2 b3) forms another 2 bit binary number that specifies a column of the matrix. The row and column lead...
4. For tER, we define ft : RR by file) = { if ( 2 ) (a) Show that ft can be written as a power series about r = 0, which converges in some interval (-r,r). (b) For 2 <r, we define P.(t) (n = 0,1,2,...) by fo(t) = ŽP.com Explain why R, P.(t) =et R P.0 and use this to conclude that Pu() = (2) M(0) +. In particular, each P is a polynomial of degree n. These...
Please show work 1.For the function f(x) = ln(x + 1) find the second Taylor polynomial P2(x) centered at c = 2. (9 points) 2. Use the Maclaurin series for arctan x to find a Maclaurin series for f(x). 3. Find the radius of convergence and the interval of convergence of the power series. We were unable to transcribe this imageWe were unable to transcribe this image
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the sine terms, and can be approximate an odd function, so Fo(x) b sinx)+b2 sin(2x)+ b, sin(3x)+. Why is there no b, term in the series F, (x)? 1. 2. Using steps similar to those outlined for even functions, develop a rule for finding the coefficients to approximate any odd function on the interval [-π, π]. 3. If f (x)sin...
For parts a, b, c and d, use the following function: f(x) = e-5x a) (3 points) Write the Taylor polynomial of degree four for f(x) centered at 0. b) (2 points) Use the Taylor polynomial from part a to estimate the value of e-0.5. (Hint: let find x). c) (3 points) Write the series generated by f(x) at zero in sigma notation. d) (3 points) Find the radius of convergence and state the interval of convergence. d) (3 points)...
Problem 3 (7 points) Define three functions A,A,As as follows: βί(x) = 0 whenever x < 0 and A(x)-1 whenever x > 0, Moreover we let A (0)-0, β2(0)-1 and A3(0) . Let f be a bounded function on [-1, 1] (a) Prove that f ER(B1) if and only if lim0+ f(x)-f(0). In this case prove that 1 『(0) elf, -1 (b) State and prove a similar result for A. (c) Prove that f ER(B3) if and only if f...
11. Find the nth Maclaurin polynomial for the function a) f(x)e2,n 3 b) f(a)cos3x, n 4 12 Find the intommlc 11. Find the nth Maclaurin polynomial for the function a) f(x)e2,n 3 b) f(a)cos3x, n 4 12 Find the intommlc
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand its derivatives satisfy the equation where f(x) denotes the rth derivative of f(x) and f (b) Show thatf0(n2p2)f(m)(o) (x) is f(x). (nt2) (nti) (I-x) (nt 2 e 0 (c) For p E R-仕1, ±3), find the MacLaurin Series for f(x), up to and including the...