Consider the sequence {fn(x)}, where sin(nx) fn(x) = 1+ nx a. Show that fn(x) converges pointwise to f(x) = 0 on [1,0)

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A: Given- Six students A, B, C, D, E, and F went to the library once last Monday night. One of them sto...

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Q: Task 24 Proof the Poincaré-inequality in the n-dimensional case.

A: I have solved the abive question below please do upvote if you like the solution thank you

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Q: Evaluate the ff. 1.  ∫8m^2/m^3+2)^3 dm 2.  ∫ sinθ dθ 3. ∫sec^2y/csc y dy

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Q: Lemma 2.31 Let (X, || · ||x), (Y, || · ||Y) be normed vector spaces and F E L(X,Y). Then ||F||c(x,Y)...

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Q: 4. Let h(x) = V 1+x* . Rotate the region bounded by the x-axis, y = 1+ x* for -15xs1 about the x-axi...

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Q: Is the set of rational numbers a group under the operation of addition? Is the set of rational numbe...

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Q: Consider the parabola given by the equation: y = x + 8x – 2 Find the following for this parabola: A)...

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Q: O (1,0) Find the solution of the initial value problem ry + y(#/2) = 1, r> 0. Answer: -2(T(4) -1 I C...

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

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Q: Express (-5 – 2i) in polar form. 29/158.2 O 29/201.8° O v21Z21.8° O v21Z68.2°

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A: Given differential equation is exactly differential equation. 

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Q: (1) Find A = LU, where L is a unit lower trian gular matrix and U is an upper triangular matri: (by ...

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Q: 3) Given the function f(x) which is used to determine the draft pressure fluctuations coming from a ...

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Q: Simplify -3- -4•/-72 O8 3i O 12v6i 2-12 6i

A: Please find the detailed solution in below image. The answer is 3rd option :    -12√6 i  

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Q: Find the Inverse Laplace Transform, F (s) = (s-2)(s-3)(s-6)

A: The given question is related with inverse Laplace transform. Given that,                   Fs = ss-...

Q: Solve for the solution of differential equation using Laplace Transform. y – 5y +6y = 0; y (0) = y (...

A:  Correct ans is option = D Please find attachment for the details solution

Q: 7s+15 Find L-1 s+2 O 7 cos (v3t) + sin(v3t) O 7 cos (v2t) + sin (v2t) O 7 cos (v2t) + sin(v2t) O 15 ...

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Q: Is the set of numbers described below a group under the given operation? Prime numbers; multiplicati...

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Q: trace(A)

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Q: Solve the following set of equations using the Gaussian elimination method: 4x1 + 2x2 − 2x3 = 8 x1...

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Q: c an sin d an = n (1 +(-1)")

A:   As given by the question There are given that the sequences: an=sinnπ4 Now, From the properties of...

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Q: Let T be the tetrahedron with vertices (3, 0, 0), (0, 3, 0), (0, 0, 5) and the origin. Write z) dV i...

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Q: An integrating factor of y+ x+ xy² dx+ x* |dy = 0 is 3 2 4 1 A) B) x3 1 C) - D) x2

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Q: Find the Laplace Transform. f (t) = {1-3t for 03

A: The solution is given as 

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Q: Determine the value of the integral: x² dx. A) 0 B) 234 C) -234 D) 702

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Q: 3. The power P in watts (W) in a circuit with resistance R in ohms (N) 36R varies according to P = R...

A: The function has to be P = 36RR + 42. So, we are solving the question by taking this function Given-...