4. Consider the function f(x) = sin(x), x > 0. (a) Estimate f(r) - f(A), where TA is an approximation to rr. (b) Estimate Rel(f(A)) in terms of the error Rel (TA). - f(TA 4. Consider the func...
The Taylor polynomial approximation pn (r) for f(x) = sin(x) around x,-0 is given as follows: TL 2k 1)! Write a MATLAB function taylor sin.m to approximate the sine function. The function should have the following header: function [p] = taylor-sin(x, n) where x is the input vector, scalar n indicates the order of the Taylor polynomials, and output vector p has the values of the polynomial. Remember to give the function a description and call format. in your script,...
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...
3. Consider the periodic function defined by f(x) =sin(r) 0 x<T 0 and f(x) f(x+27) (a) Sketch f(x) on the interval -3T < 3T (b) Find the complex Fourier series of f(r) and obtain from it the regular Fourier series. 3. Consider the periodic function defined by f(x) =sin(r) 0 x
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the equidistant points r--r/4, xi =-r/8, x2 = 0, 3 π/8, and x4 = π/4. Estimate the maximum of the interpolation absolute error for x E [-r/4, π/4 , ie, give an upper bound for this absolute error maxsin(x) P(x) s? Remark: you are not asked to give the interpolation polynomial P(r). 1. Consider the polynonial Pl (z) of degree 4...
Consider an electron whose wave function is ?(r,0,?)-- e* sin ? + cos ?)f(r). 47t where I (rrr2dr-| , and ?, ? are the azimuth and polar angles, respectively. (i) Rewrite the wave function in terms of the appropriate spherical harmonics. (4 marks) (ii) What are the possible measurement results of the z-component L, of the angular momentum of the electron in this state? (6 marks) (iii) Calculate the probability of obtaining each of the possible results in part (i)....
8pt (4. Let f(x) = 4+0+ sin a. (a) Find the linear approximation L(x) of (a) at a = 0. reo)= (4+0+0= dusa (0) +csx) : ' +wJy -' *wslo), ? zru txtsinx ? Ju+x-sior ? Surotu u TPH (b) Use the linear approximation from part (a) to estimate (06) 0.5 0.06 30 2 + 1 (x-6.06) 2 + 1 x .03 - 2 (x+1896 pt ) 0.030
Consider the function: f (x) = b - sin(x), where bis an arbitrary number. Are roots always possible for any value of b? Yes No Consider the function: f (x) = a - tan(x), where a is an arbitrary number. Are roots always possible? True False
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3 x2 -9x + 20 Evaluate the following limits You do not have to cite limit laws, but you must show how you arrived at your answer If a limit Does Not Exist, explain why. You should use oo or -oo where applicable Calculating the limit using L'Hopital's Rule will receive NO CREDIT. (a) lim f(x) r-+0 (b) lim f(x)= z-1 (e) lim f(z) (d)...
use radians in trig functions Estimate the slope f (3.5) for f(x)-sin(3xusing: a. Forward difference approximation with h 0.2 b. Backward difference approximation with h 0.2 c. Centered difference approximation with h 0.2. For each estimated slope, provide the true percent relative error, & Which approximation is the most accurate? Box your answ ers
Please show all steps with clear hand writing 3. Consider the periodic function defined by sin(x) 0<x< f(r) = and f(x) = f(x + 27). (a) Sketch f(x) on the interval-3r < r 〈 3T. etch fx on the interva (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series. 3. Consider the periodic function defined by sin(x) 0