P: R → Ris an isomorphism. then for all € R' which of the following is true. a. (x) = x b. (x) = tan(x) с. (x) = a2 +1 d. $(x) = log(æ)

Q: 4. (a) Prove that H, { f(x) [Hn-1{f(x)} + Hn+1{f(x)}] and hence find T. 2n S (x – a) Hn ,a > 0, k >…

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Q: Please solve this question

A: Note: Properties of trace: Let A and B be two matrices. trace(A+B) = trace(A) + trace(B). trace(αA)…

Q: (c) Compute of using the Chain Rule. of дf дх дf ду дf dz. + дя дх дя ду дя дz дя (Use symbolic…

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Q: The linearization a at a = 0 to √8+7x is A + Br. Compute A and B. A B=

A: To Find: Linearization for fx=8+7x at a=0

Q: If Osf(x)s g(x) on [a, ∞) and | g(x)dx is divergent, then | F(x)dx is divergent. Select one: O True…

A: We have to state true or false.

Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by f X,Y (x, y) = (x+y)/21…

A: The given joint pmf of X and Y can be described as X.       Y 1 2 P(X = x) 1 2/21 3/21 5/21 2…

Q: If the Wronskian of f and g is t cos t - sin t, and if u = f + 3g, v= fg, find the Wronskian of u…

A: It is provided that the Wronskian of f and g is tcost-sint. We need to determine the Wronskian of u,…

Q: If la,} and {b„} are divergent then {a, + b,} is divergent. True False

A: Given: an and bn are divergent . The objective is to state whether an+bn is divergent is true or…

Q: 3. Let L be a linear operator on R and let L(1) = a . Show that L(x) = ax for all x E R .

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Q: The inverse z-transform of (a) (-a)" [] 2₁] e-a-3 (z-ea)(z-3) -, a>0 ROC: ea <z<3 is,

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Q: Vx E X, (x, x) ¢ R. X = {1,2,3}, h of the following relations R on X is irreflexive?

A: Here given set   X={1,2,3}   we know that relation is irreflexive when each x belong X (x,x) dose…

Q: Find laplase transform F(s) if f(t) as shown

A: In this question, we need to find the Laplace transform of the given periodic function with period…

Q: Find the z-transform for each of the following sequences: а. x(п) b. x(n) = 10sin(0.25an)u(n) 10u(n)…

A: Solution

Q: 3. Show that every y E lị defines a continuous linear functional on l through the inner product,…

A:

Q: Prove that the family of operators T (t): L2 (0,1) → L2 (0,1), t > 0, where T (t) p (x) = 0 for 0 <r…

A: Let T'=Tt:L20,1→L20,1 be an operator for a fixed t≥0. To prove that this operator is a strongly…

Q: lim (z,y)→(0,0) (3 + (x² + y²) In(x² + y?)) 00 does not exist O 30 1,

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Q: If (p) is the Fourier Sine transform of f(x) for p>0, then prove tha Af(x}} = - (- p) for p<0.

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Q: a) Let f: Z Z be such that f(x) 2*x. Is f invertible, and if so, what is its inverse?

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Let f(x, y, z) = x³e" Vz² + 5 and let x = rt², y = r2t², and z = sin(t) cos(r). (a) Draw a tree…

A:

Q: Please solve this question.

A: We are given that L(p(x)) = p(0). Let p(x), q(x) in P4(F) and α, β in the field F. Now,…

Q: 5. (a) Make a tree diagram for the chain rule for f(x, y, z) = x²y² + y²z² + x²z², x = rt, y = r²t³,…

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Q: 4 (1 + cosh(t))2

A: Introduction: Laplace transformation is important in the design of control systems. It is necessary…

Q: 3) Prove that the multiplication map · : Z/nx Z/n → Z /n given by [x] · [y] = [xy] is well-defined.

A: To prove that the multiplication map · : ℤn×ℤn→ℤn given by    x·y=xy  is well-defined.

Q: (1+*)"- TL limn TL O a. V2 O b. 00 O c. 1 O d.e v2 O e. does not exist O f. V2 9. ev2 Ch. 0

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Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: 8. Prove the following properties of the Fourier convolution: (a) f (x) * g (x) = g (x) * f (x), (b)…

A: As per our company guidelines we are supposed to answer only first 3 subparts, kindly repost other…

Q: (a). If x = 0 and y > 0 (y 0, then Arg z = tan-(y/x) E (-T/2, 7/2). (c). If x 0 (y < 0), then Arg…

A: Arg(z1z2) =Argz1 +Argz2 if and only if argz1 +argz2  lies between -π and π

Q: Compute the Laplace transform Lf (s) of the function f (x) = x2eαx for s &gt; α.

A:

Q: Suppose w=x/y+y/z, where x=e3t, y=2+sin(t)x=e3t, and z=2+cos(6t). A ) Use the chain rule to find…

A: w=xy+yz, where x=e3t, y=2+sint &amp; z=2+cos6t Partially differentiating w=xy+yz with respect to x,…

Q: (a) express ux, u y, and uz as func-tions of x, y, and z both by using the Chain Rule and by…

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Q: Let AC C([-1,1]) be defined by A = {f€c'(I-1, 1), f(0) = 0, f'(x)| < 1, V x€ (-1,1)} Prove that A is…

A: The set A is defined as A=f∈C1-1,1, f0=0, f'x≤1, ∀x∈-1,1. To prove that A is relatively compact.…

Q: Prove that the family of operators T (t): L2 (0,1) → L2 (0,1), t > 0, where T (t) p (x) = 0 for 0 <r…

A: Fix an operator Tt:L20,1→L20,1, for a fixed t. To prove that Tt is a strongly continuous semigroup.…

Q: If T: H→→H is a bounded self-adjoint linear operator and T‡0, then T"#0. Prove this (a) for n = 2,…

A: Given T:H→H is a bounded self-adjoint linear operator and T≠0. We know that if T is a self adjoint…

Q: Find the Fourier Transform of Hence Prove that f(x): cos(sx) + Ssin(sx) 1+s² -ds = x 0 OEIN 0 2 Tex…

A: Introduction: Through Fourier transformation, a real-time function can be converted into a complex…

Q: Suppose that w = f(x, Y, 2), x = h(s,t), y = g(s,t), z= k(s) and all the conditions required for the…

A:

Q: When using Laplace transform to solve the IVP :Xn = 'n u(x,0)= - x. t>0 Then u]= 1 - SX e a. SX ce…

A: Given ut=ux, -∞&lt;x&lt;∞, t&gt;0, ux,0=-x

Q: 2n Jnsi (x) = " J,(x) – J(4)

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Q: 2. Consider an operator of the form (Lf) (x) = Ef(x;)g;(x) where a O for all a E [a,b] and for all…

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Q: suppose x (t) hasFourier transform X (w) = e^¯w find Determine transforms of x (2t) and x (t + 1)

A: Fourier transform of these functions are found by using properties of Fourier transform.

Q: If the Wronskian of f and g is t cos t - sin t, and if u = f+ 2g, v = f - g, find the Wronskian of u…

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Q: Find the inverse Laplace transform f(t) = L-' {F(s)} of the functic 5 3s F(s) = s2 + 16 s2 + 49 } 5…

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Q: Consider the following operator A : L²[0, 1] → L'[0, 1] A(f)(x) = (f(x))² + f(x). If this a linear…

A: Given, the operator  A : L20, 1→L10, 1 defind by                               A(f)(x)=(f(x))2+f(x)…

Q: Let f(x) = sin x and g(x) = cos x, and W = span{f,g}. Use the Wronskian to show that f and g are…

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Q: Prove that the Generating function of Bessel function i.e. £1J„(x)t" = e*/2(-1/2), %3D

A: Let ϕx,t=ex2t-1t. Let us prove that ϕx,t is the generating function of the Bessel function…

Q: Let M, = Z, – Z;-1, Zo = 0, where {Zn, n21} is a martingale. Show that E(M,„Z„-1] = 0

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Q: -i log(U) is Hermitian and therefore that 4. For a unitary operator U, show that T = U = el for some…

A: Let U be a unitary operator.  To prove that T=-ilogU is Hermitian.  Since, U is an unitary operator,…

Q: Find the la place transform of (e²=²+) le. e-e 2

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Q: 1. Let T: C(R) → R be a linear map with domain all continuous functions on R and codomain R. If…

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Q: O: Find the general kolution ay ofte 1SE 1Order ODE of x²dY= Y- xy de

A: