Let f: RR be a continuous 27-periodic function whose Fourier series is +∞ 1 1/2 + + /20 cos(nx). n=1 Then the quadratic norm of f equals (A) T (B) 2 (C) √ (D) √2T

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A: Solution :-

Q: Find the General Solution of (D² + 5DD' +6D22)Z = 10 cos(x - y)

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Q: Solve the boundry-Valued PDE 24 = 4 ठेप by ulo¹y) = 8e³y using the genral method ans: u(x,y) = 8…

A: The given PDE is                                ∂u∂x=4∂u∂y with                      u(0,y)=8e-3y

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Q: 8 2 Let (an) be a numerical sequence such that an>0 and 71-0 an+1 (A) lim 0 n→∞0 an (B) an n=0 8 (C)…

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Q: Evaluate: ₁[2³(x + y)³] dz dy dx

A: The given integral is                       ∫-43∫-12∫01z3(x+y)3dz dy dx

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Q: X ди Әх || ди u + Y əy

A: The given differential equation is             x∂u∂x=u+y∂u∂y

Q: 8 3. Then 4 Let f be the sum of the power series √1+5n n=0 (A) ƒ"(0) = √11 (B) ƒ(7)(0) = 0 (C) the…

A: Given that  f be the sum of the power series  ∑n=0∞11+5nx3n. The correct option is (B).  f(7)(0)=0

Q: F (ƒ') - {¹(- Ji(- (-5w+4w2), (a) Find an expression for f (w) in terms of unit step functions u w…

A: Let us start solving the problem step by step  We must find the values of f(w) F(x) and g(x)

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Q: A. Sequences 1. Given that a2 = 6 and a€ = 96 are terms of a geometric sequence, find a4. 2. Given…

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Q: Let A = {1, 2, 3, 5, 6, 10, 15, 30} and define R on A by xRy if and only if x divides y. a. Find…

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Q: B A 20⁰ D с Goven LBAC = 20° AB = AC AD = B C Find LADB

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Q: 3 Evaluate: ³₂²₁²[z³(x + y)³] dz dy dx

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Q: Evaluate ¬⇒(PV¬q) if p and r are True and q is False. Select one: O True O False

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Q: Find the area of the region above the curve y = x2-6, below y= x, and above y=−x.

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Q: (a) Find the SVD form of the matrix [1.2 0.9 -4 A = 1.6 1.2 3 (b) Use the SVD to determine the…

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Q: FIND Y(S) OF THE GIVEN EQUATION. 2y" + 3y' – 2y = te-2, y(0)=0 y (0) = -2 y" - 10y' +9y = 5t, y(0) =…

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Q: Evaluate ¬⇒(PV¬q) if p and r are True and q is False. Select one: O True O False Tim

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Q: Solve the following systems of linear equations via matrix algebra: –3x + 2y – z = –1 6x – 6y + 7z…

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Q: 9. Determine y = Yc+yp using Non-homogenous equations: Method of Undetermined Coefficients Given: y"…

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Q: Determine the total solution of the differential equation (D2+5D+6)y=6e(-3x)-100e2x O A. y =…

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Q: For each of the differential equation determine the order of the equation and if the equation is…

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Q: 130. y" = 3y + xe xẻ -x

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Q: 8 Given kER, the function f(x, y) = kx² + (k − 1)y² + 12.ry admits (A) a minimum point, if k = 0)…

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Q: 7 The volume of the solid region 7 = Is (A) 120T (B) 100T (C) 132T (D) 967 {(x, y, z) € R³: 4≤2² +…

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Q: 02u at2 = ә2u аг 0x2

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Q: <% Define frew = {ecretastipur/a Solve: ५ (3) 3) _ २५(3) + ५ - २५ = fa) ५(0) = 1, ५' (0) = 2, ५"(७)…

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Q: A hemispherical tank of radius 6 feet is positioned as in the figure below. How much work is…

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Q: (x² + y2). Draw the solid R. ve the cone z = √3x² + 3y² and below the coordinates. Draw the solid B

A: To set up the triple integral as,

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Q: . Every function has a fixed point (TRUE OR FALSE?) B. The number 3.141529 estimates 3.141516 to…

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Q: 1 Which of the following complex functions is holomorphic in C? (A) f(x+iy) = y for every z € R, YER…

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Q: II. Solve the non-linear equation: 1.) x2 - xy + 2y2 = 16 x - y = 2

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Q: 6. Evaluate the line integral ² dr+z²y dy where C' is the rectangle with vertices (0,0), (5,0),…

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Q: Evaluate the integral: S/2 Se S77/2 S¹² sin (=) dt du π/2

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Q: 4. Using the following matrices solve then verify the following properties: 3 0 4 A = --} -- 1 -- :…

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