2. An even function f(t) has Fourier coefficients ao = 1 and an = 2 and period 27. Use Parseval's theorem to evaluate ff(t)|²dt? [hint, En_12" = iz]

Q: then prove that i) F, [ƒ (x) cos ax] = [f, (p + a) +f, (p a)] 1 ii) F.[f(x) sin ax] 2 [f. (p + a) –…

A:

Q: Differentiate the function. f(x) = sin(x) In(4x) f'(x) =

A: ddxu(x)v(x)=v(x)ddx(u(x))+u(x)ddx(v(x)) ddx(sin(x))=cosx ddx(ln(ax))=aax=1x…

Q: 8(x – a) + 8(x + a)

A: Topic:- calculus

Q: Find the Fourier approximation with the specified order of the function on the interval [0, 2π].f…

A:

Q: Find the Fourier Transformation of II (t-) Select one: O l sinc(f) O ef sinc(2f) O jrf sinc(f) 3jef…

A:

Q: f(x) = [sin x if 0 T

A:

Q: √4x+4-√√5x+1 x#3 Q18) if f(x)= x-3 k x=3 A) 15) 1 C)O by Q19) Use local linear approximation in ind…

A:

Q: 921) Which of the following is an odd function A) cos xsin x 11 sec.x C). DUNK DOOV

A:

Q: Find the finite difference formula for the second derivative at point x=x; with points X₁, Xi+1,…

A:

Q: f(x) = -12-21x + 18x^2 - 2.75x^3 what method will give a root of the function equal to - 0.287425 in…

A: We will use a numerical method to determine what will be the value of root of the given function in…

Q: Compute the coefficient Fourier an of the *-1, 0<r <a S(2) = { 0, *<I< 27

A:

Q: Determine if the setsin² {sin²x, 1-cos(2x)} is linearly dependent or linearly independent on I =…

A: Let B={sin2x,1-cos(2x)}.

Q: 235 óf the textbc (d) F{e* ,5iz-az²

A:

Q: kpression for "12 times x."

A: Times means multiplication. Sometimes it is denoted by dot.

Q: Q17) The slope of the tangent line of the curve x² + y²=5 at the point (1,-2)- A) √√4x-4-√√5x-1 x-3…

A:

Q: Consider the function f(x) = cos(2x) for -2pi &lt; x ≤ 2pi and zero otherwise.A) Show that it meets…

A:

Q: Prove that Fourier cosine transform of f(x) = cos(x), 0<x<3 is: 1/27 (³ sin 3(p-1), sin 3(p+1) p-1 +…

A: Introduction: A Fourier remodel (FT) is a mathematical remodel that decomposes features relying on…

Q: Find the Exponential Fourier coefficient Cn for signal f(x) = x Defined on interval [-1 ,1]

A: Complex form of Fourier series is defined as follows: fx=∑n=-∞∞cne-inx2πL where,…

Q: ∞ sin2x dx (x²+1)²

A:

Q: Let f(x)=2 cos(5x)+3 sin(4x) and let q, be the Fourier polynomial of degree n for f. (a) Show that…

A: Given: fx=2cos5x+3sin4x The period is 2π as f2π+x=fx The fourier polynomial of degree n is:…

Q: Find a harmonic function o on the upper half-plane that takes values ø(x) = 0 for |a| > 1 and $(x) :…

A: Sol

Q: Determine two funetions f and g whose produet result in (f x g)(=) – 8 sin"I+ 27.

A: see below the answer no need of explanation

Q: Let f(x) = (x2 + 1), n<x <a be a periodic function, then the Fourier coefficient az = Answer:

A:

Q: skla 8. What is the value of Fourier discrete function & [k] at k = 1?

A: To determine: The value of the Fourier discrete function δk at k=1.

Q: 8. Find the 6th order Fourier approximation of the function that is periodic and f(x) = x, -2<x <2

A: Given function is fx=x ,   -2≤x≤2 Compare the interval  -2≤x≤2 with -L≤x≤L, we get L=2…

Q: The functions g(b, c, d) and h(b, c, d) are defined as: g = (b+ c+ d')' + (b' + c' + d') · (b' . c'…

A:

Q: Consider the function f(x) = cos(2x) for -2pi &lt; x ≤ 2pi and zero otherwise.A) Show that it meets…

A: A) Condition for Fourier Transform To have a Fourier transform, a function must be absolutely…

Q: 3) Let f(x) =) () Find the fourier Senies of fx nd skatch the the sum function on [-37,37). +++*…

A: we know Fourier series f(x)= 90+∑ n=1∞ancosnx+bnsin nx…

Q: times the Fourier transform of f(x) provided that the first (n – 1) derivatives of f(x) vanish as…

A: