Let f : R → R be a 27 -periodic integrable function and let E-, Cneina be the Fourier series of f. Which of the following is true? Select one: a. Co may not be in R . b. Cn ¢ R for every n E 2N. C. Cn E R for every n E N. d. None of the ot ers are true. e. Cn ¢ R for every n E 2Z if f is even.

Q: Using De Moivre's theorem determine z= 3+6i^4

A:

Q: Fourier Series Please explain the gragh when the k changing

A: Given: x^t=∑k=-KKakejkω0t Plots of x^t as approximated by K=1,5,10,30 terms, superimposed on top of…

Q: Evaluate the in tegsal uing vesidues and de +. other method which any can be applied to selve this…

A: Solving by other Method: Given Integral is : ∫0∞dx(x2+1)2 Now, we have a reduction formula,…

Q: Find the Laplace Transform of the function. Show your work. f(x) = sinh(ax)

A:

Q: 7. xy + y = x², x > 0 8.

A: The solution for the asked question is given as

Q: 4. Interval 0<x<n, function, f(x) = sin 2x. %3D

A: We have to find the Fourier series of the function fx=sin2x ,x∈0,π

Q: The Debroglie wavelength of an electron * .with a velocity of 1.00x 10^6 m s-1 mass of electron is…

A: Debrogile wavelength:

Q: Fourier Integral Get a representation of the Fourier integral a)                f(x){…

A:

Q: Subject: calculus Find inverse laplce of (s)/(s^2+a^2) by integration formula

A:

Q: V sec3(In x) + sec2(In x) tan(In x) dx Given: 2x Find: du O tan(in x) dx X O tan(In x) dx 2x sec (In…

A: Given:     To determine: expression for du

Q: Using the concept of differential approximates the value of sqrt(85)

A: Given value is 85 We have to find its approximate value using differential approximation

Q: (X) dx

A: We have to find the integral of the product of the associated legendres.

Q: Suppose the area of the region enclosed by f(x) = x - 1, y = 0, x = 2, x = 7 is approximated by…

A: Consider the given:  fx=x3-1y=0x=2x=7 Consider the graph:

Q: c) Sketch the Fourier transforrm of two identical sinc functions centered at ± X1.

A: The given function is, ±xt The Fourier transform of  sinc function  is rect function.

Q: 5. Interval 0 <x<n, function, f(x) = cos x.

A:

Q: 3s-1 -1 s2-6s+16)

A: Recall: L-1bs-a2+b2 = eat sin bt L-1s-as-a2+b2 = eat cos bt

Q: sec"xdx V1-4tan?x

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate I cose cosec² (20) cot (20) do.

A: As per the question we are given an indefinite Integra which we have to evaluate.

Q: f(x) = x*exp(-ax²)

A: Given function is f(x)=xe-ax2 Since we know ℱe-ax2=12ae-ω24a

Q: Inverse identity Show that cosh (cosh x) = |x| by using the formula cosht = In(t + Vr - 1) and…

A: Given : cosh-1(coshx)=x for all x   and  cosh-1t=ln (t+t2-1)    Claim :…

Q: sin (U+y) (a,y)そ(。2) %3D

A:

Q: 2) v = (z* - 2z + 1)ž

A: Given: v=z4-2z+132

Q: INTEGRATION OF 1/1+TANX

A:

Q: Filling a pool A cross section of a rectangular pool of di- mensions 80 feet by 40 feet is shown in…

A: Given a cross section of a rectangular pool of dimensions 80 feet by 40 feet.

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.