Evaluate ax xm-1 sin bx dx in terms of Gamma function. -ax

Q: 2. Use Laplace Transform to find (f * g)(t) if ƒ(t) = e=t and g(t) = sin(t).

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Q: The equatiokn  Y = (x,y)T  is given as a vectorfunction with 2 components and A = table below 3 2 2...

A: Given is a matrix A and we have to diagonalize the matrix A. First we find eigenvalue of matrix A an...

Q: 7-52. Curves to parametric equations Find parametric equations tor the tolowing curves. Include an i...

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Q: #12 only

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Q: 5. Use induction to prove that for every n E N we have E(k · k!) = (n + 1)! – 1 k=1

A: We want to prove ∑k=1n(k·k!) = (n+1)! - 1

Q: Use Stokes's Theorem to evaluate JcF•dr. Use a computer algebra system to verify your results. C is ...

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Q: Consider the simplex tableau given below. X1 X2 S1 S2 1 4. 0. 3. 3 3 0. 1 32 - 9 4 1 (A) The pivot e...

A: We have to determined the followings from the given simplex tableau.

Q: Find the Orthogonal Trajectories: a.) y6 = C (x2 + 1)

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Q: 3. Given the matrix B below, 2 31 2 -1 3 2 B = 4 3 1 2 3 2 0 71 Solve for det inv B.

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Q: (a) The maximum carrying capacity of a park is 100 animals. Currently, there are 10 animals in the p...

A: The detailed solution of the problem follow the next steps.

Q: Find the volume of the solid formed when the area of the region bounded by Vx2 + y²=1, y+1=0,y-1%=D0...

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Q: Example 2: Evaluate numerically I= f fxye dydx.

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Q: А. X+dy =3 2x -3ÿ =-8 B. x tay +2 =-2 X tdy +Z=-2 -2メ-39-2 = dx +4y tQz==4 ミ9

A: As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem....

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 1 + e4t L{f(t)}

A: Given function is f(t) = 1 + e4t

Q: Evaluate the following telescoping series or state whether the series diverges. 1 1 Σ (n+1)* 102. 13...

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Q: 1. What is the Laplace transform of f(t) = te' ? A] F(s) = s + e B] F(s) = 1/(s–1)² c) F(s) = 1–s/s²...

A: Given, f(t)=tet. The Laplace transform for the function f(t)=tneat is given by n!(s-a)n+1, where n=1...

Q: Q6) by using the (graphical method) find the optimum solution of X1, X2 that the minimum Z=10X1+25X2...

A: Given ,   min Z = 10X1 +25X2 subject to the constraints,  4X1+3X2 ≤ 9                               ...

Q: Given the point D(−4, 5, 3) and A = yax + (x + z)z ay, express the D and A in: Kindly answer in vec...

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Q: S-4 2) F(5) = In

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Q: Let 1 -1 0 0 0 -1 0 -1 0 1 1 A = 1 -1 a. Draw a directed graph having A as its incidence matrix b. F...

A: Here, we are given the following matrix.      A=1-1000 100-10 010-10 0010-1 For (a), We know that in...

Q: - Solve Homogeneous Ux =4 UxX,ucoit)=0 u(lo,t)=0 らoo(Xくら uC以io)-「。 X 5 <8 Tlo

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Q: Determine whether the following matrices are in echelon form, reduced echelon form or not in echelon...

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Q: S t 52) dz = 6 5 6 5 6Vz - Vz O A

A: Given integral is ∫2z23 - 3z3 + 5zdz

Q: d'y +45 - 6y = -12 ; y (0) = 1, y (0) = 4, y" (0) = -2 %3D %3D dt3 dt? dt

A: We have to find the solution.

Q: Determine the value of the series E - n1 n² + 9n + 20 b)1 c)0 d) e)3

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Q: Example 5.8. Solve du 0 0, ax2 at for (i) u(x, 0+) = f(x), (ii) u(0, t) = 0, t > 0, (iii) u(1,t) = ...

A: To solve: ∂2u∂x2=∂u∂t, 0&lt;x&lt;1, t&gt;0 And, the boundary conditions are: ux,0+=fx, u0,t=0, t&gt;...

Q: What is the magnitude of the simple gain term for the following open loop transfer function: 24 G(s)...

A: Solution

Q: Find the directional derivative of f(x, y, z) =

A: Given,        f(x, y, z)=xy2+yz3 and            a=i^+2j^+2k^  

Q: Given the following vectors and points, transform each to spherical coordinate system. 8åx at (4,1,3...

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Q: Using Truth Tables, show that the following premises leads to tautology: (A A -C) v ((B v C) v -(C v...

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Q: (c) Solve the difference equation Yt+2 – 4YŁ+1 + 4Y; = 2(2*) + t² - Given initial values Y, = 2 and ...

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Q: 2 x = 8 - y, x =y - 8

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Q: 4w dw = w2 –4 -3^(5/3) О з(3/5) 3^(3/5) 3 O O O

A: We have to evaluate the integral ∫124ww2-43dw.

Q: 1?+3 v (1) =: 4/ 5t +8 5<t< I5 Where t is in seconds and v is in m/s. Using Simpson 1/3 Rule using h...

A: Here the given function is                                     vt=t2+3;     1≤t≤545t+8 ;   5&lt;t≤15...

Q: SOLVE THE FOLLOWING dy dx 4x2-4x-5 2= /(x2 – 2x + 3) 2. dy 3. dx x+1 1.

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Q: find a vector of length 5 unit that makes angle 76° with Y-axis and 25° with Z-axis ?

A: To find a vector of length of 5 units that makes angle 76° with y-axis and angle 25° with z-axis.

Q: Q: Prove the trans farm; formula's by definition f Laplace -sto L 181t-6)J= ë* (Dirac Delta Funchan)

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Q: solve one real root of e* – 2x – 5 = 0 with æo = -2 using the Fixed-Point teration Method until abso...

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Q: In a straight line the slope approaches zero as the line comes near the point X,Y. a. Cannot be dete...

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Q: 4. Let a be an odd integer. Show that (i) 8| a² – 9; (ii) 16 | aª – 81.

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Q: 1 -1 Suppose adj A =|-1 Compute A. Show all work. 1 4 (Hint: Don't confuse adj A with A.)

A: Here given that adj A=   0  1-1-1  5   0   1  0   4. We have to find A-1.

Q: Find the general solution to the following vector DE. 1 æ[t) = | -2 1

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Q: Apply Lagrange's formula inversely to obtain a root of the equation f(x) = U, given that f (30) = - ...

A: given f(30) =  -30 . f(34) = -13 , f(38) = 3 , and f(42)  = 18 here x0 =30 ,x1 = 34 ,x2= 38 ,x3 = 42...

Q: An adventurous aardvark is a card shark and gambler. He offered to let you play in a game with him. ...

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Q: n Vn (k) (-1)"-1 n + 1 n=1 n Vn +1 – Vn – 1 Σ - (1) n n=1

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Q: Calculate M6 for f(x) = 6 · In(x³) over [1, 2]. M6 %3D

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Q: T Fnd the inverse (dont we parhal ) FG) = 35 (34)5 frachion

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Q: If p times tne pth term of an A.P. is equal to q times the qth term of the same A.P., then show that...

A: let first term = a  and common difference = d

Q: Suppose z is implicitly defined as a function of x and y by the equation cy z3 – xevz + y sin rz = 3...

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Q: 6. Maximize 10x +35y subject to 8x + 6y < 48 (board-feet of lumber) 4x+y 20 (hours of carpentry) y 2...

A: Given: max 10x+35ysubject to8x+6y≤484x+y≤20y≥5x,y≥0