Determine the Laplace transform of the function F(t) = t^l.5 exp{-2t}.

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A: By the Alternating series Remainder theorem we have |S-Sn|<RN<=bN+1.

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Q: A relation is graphed on the set of axes below. Based on this graph, the relation is A. a function…

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Q: Is it possible to make Z into a vector space if we redefine addition?

A: To check: the possibility to make ℤ into a vector space.

Q: 1. Find the Laplace transforms of cosat – cos bt (a) t°sinat (b)te“ sin3t (c) +tsinat t sint sin5t…

A: 2)  We need to use Laplace Transformation of the second derivative to derive the following…

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Q: Problem Show that solving the system of nonlinear equations with the unknowns r1, 12, 13, T4 (x1 –…

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Q: Problem 2. (i) Consider the normalized vector v in R3 and the permutation matrix P, respectively 1 v…

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Q: Evaluate the definite integral. 4 6x (Simplify your answer)

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A: angle with a curve at a point means angle with tangent line at that point of curve .

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Q: For for any pestive integor n Show that %3DFHE nth fibonacci term fn=the

A: We need to show that , for any positive integer n ,  f1 f2 + f2 f3 + ....... + f2n-1 f2n = f2n2…

Q: a) A triple integral I is written using spherical coordinates as follows, p* cos o sin o d0 dodp. i)…

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Q: Solve the following integral: =* dzdy I = R where the region R is: 1. (x, < 2.x, -< xy : Consider…

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Q: Evaluate F dr, where F(x, y, z)= xyi +4zj +3yk and C is defined by the intersection of the plane x+z…

A: Given: F=xy i→+4 zj→+3y k→ c=x+z=5,    x2+y2=9 Evaluate ∫cF.dr Apply Stokes theorem ∫CF.dr=∬curl…

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Q: A-Estimate J, 2e-3* dx using trapezoidal rule with four subinterval round your answer to one decimal…

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Q: idleutify the conic Seetion from the equeition:. (1) 16y-an-36n –-964-36-0 2 () n* +y" -ux +loy-7 =0…

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Q: Construct a formal proof for each argument

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Q: Solve the given differential equation. x²y" – 3xy' – 7y = 0 | y(x) = ,x > 0

A: Solution

Q: Match each of the power series below with the correct statement about it. Series A: +1 n=0 Series B:…

A: This question related to power series .

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Q: Find the center of mass of the lamina a) bounded by the curves y=x-4 and y= 5, and having density…

A: Mass of lamina bounded by region R  M=∫∫R  ρx,y dx dy Moment about x-axis Mx=∫∫Ry  ρx,y dx dy…

Q: The function 1. f(z, y) 4+4z + 4y can be expressed as a Taylor Series about z = 4. y - 5 ie. %3D 1…

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Q: Σ (-1)"-1_3 n4 * Jerror| < 0.0007 n=1 Term: n =

A: Error estimation theorem is used

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Q: ulaté the integral: I = (x + 2y) dædy where the region R is defined as: R = {(x, y) E R² :0 <x < 2,…

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Q: 85. Suppose that f is the differentiable function show panying graph and that the position at time t…

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Q: 5. Let x be a solution to the homogeneous linear system of equations Ax = 0, where A is an n xn…

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Q: b) For a general curve r: 1R, define the vectors t(s), n(s) and b(s) as t(s) - r(s) (s) and b(s) =…

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Q: Using only the Laplace transform table to obtain the Laplace transform of the following functions:…

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Q: If AWXY AHJI, complete each part. a) JI = %3D J b) JH = %3D W. 37 c) mZW = %3D 15 m d) mZJ = 114 Y…

A: Given figure is and also given that ∆WXY≅∆HJI It means ∆WXY is congruent to ∆HJI. Congruence…

Q: Diagonalizing a Matrix In Exercises 7-14, for each matrix A, find (if possible) a nonsingular matrix…

A: The given matrix is A=2-2   30   3-20-1   2 We have to find a nonsingular matrix P such that P-1AP…

Q: 3. Let S, and S, be two subspaces of R such that s, n s, = ((0,0,0,0,.0)) and dimension(S,) =…

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Q: Optimizati a) If a and b are positive numbers, find the maximum value of f(x)=x"(1–x)°, 0<xs1.

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Q: Calculate the work done by the force F(x, y) = y?î+ xyj in moving a particle along the line which…

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Q: Write the sum using sigma notation: A 1 1 1 1 2 B, where 1· 2 2·3 3. 4 180 · 181 n=1 A = В-

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Q: A clamped cubic spline for a function f on 0,3 is given by [1+ax² -2x', S(x) = . [1-2(x-1)+b(x-1)² +…

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Q: 2. Find the power series representation of the following functions. And then write out their I.O.C..…

A: We know that series expansion of 11-x 1-x-1=1+x+x2+x3+x4+x5+...... We know that series expansion of…