for 0< x < 3,Let f(=) = {°(x – 3)for 3 < x < 6.Compute the Fourier cosine coefficients for f(x).Ao-9/2*(1/3)An(-((18pinsin(pin)+36cos(pin)-36cos((pin)/2))/(pi^2*n^2)))"(1/3)AoGive values for the Fourier cosine series C(x)An cos(6n=1C(6) =-(3/4)+C(-4) :(-(3/4))• C(8) =

note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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P(A)=0.3, P(B)=0.6, A and B are indep, find P(AB'), P(A|B') ---- o
L {5-e²t + 6t²} L {t² – 3t – 2e-¹ sin(3t)} - L { t^ — t² − 4 + sin(√2t)}
Q13) {t+sin² t} = (A) + 1 [-] (D) ² + 1 [24] / (B) 3+ [4] (C) + [-] +4 (E) + [-]
Please explain how to get the 7th degree Maclaurin polynomial for xsin(x2) given that
Y1 Entered Y4 1 1 t t^2 e^(-2*t) t*[e^(-2*t)] (t^2) *[e^(-2*t)] (t^3)*[e^(-2*t)] At least one of the answers above is NOT correct. [e^(1*t)]*cos(1*t) e(-21) [e^(1*t)]*sin(1*t) 37 = 3(-21) 3/2 t Y3 2 Y5 te Ys -21 Answer Preview Y6 1²e (-21) el cos(lt) (You can enter your answers in any order.) 1 Y9 t t² -21 -21 te t²e-2t A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows. t³e-2t (²6r+18)r³(r − 3)¹ = 0 Write the nine fundamental solutions to the differential equation as functions of the variable t. elt cos(lt) e¹t sin(lt) Result correct e¹f sin (lt) correct correct incorrect incorrect incorrect incorrect incorrect incorrect
14) F(1) =(1, 4VF). a) Find the domain of 7(1) b) Sketch the graph of F(t). Indicate the direction of increasing t with an arrow. c) Find F'(1) d) Find F'(1) and sketch on graph at t=1
Q1) Show that: (a) (1+x)° =1+6x (b) :(cosx): = -sinx dx (e) (V) = d 1 1 ( VI) = (d) /1+ tan x = 1+: dx 2 Vx 2x2+2x+1 x² –1 Q2) Find the asymptotes for the following functions : f(x)=- g(x) = 1+x2 2x V1+cos 2x (1) lim,- 4(x- |4-x2| Q3) Find: (2) limx→-2- (x+ 2) 2-x Q4) Find the equation of the normal to the curve [y+x(1+y)-4] at point (2,1).
Solve for Fourier coefficient, Ssin x 02x27 f(x)= 0 T >x 22n cosx sec x + cosx csc csc² x csc? x secx cos? x cos x cos x § f(x)dx _ ? If f(x)* , then 1
If ƒ = (x+1)]√x² + y + + —_tan^(3x−y), and g = - at (0.1.4) 0,1, find: fxcurl g +(g.V) at x + y In(xy + 2)² + z(y=x²)j + sin² zy³k
sketch a graph of -4 sin(x - π) 6 5 4 3 2 1 -2π -3π/2 -J -Jt/2 -1 -2 -3 -4 -5 -6 π/2 B 3/2 2π
Show that: (AB)-1 = B-'A-1 (AB is invertible)

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