4) Using tensor formalism, i.e. Kronecker delta, Levi-Civita symbol, and Einstein's summation convention, prove the following vector identities: (a) Ā × (B × T) = B (Ä · C) – T(A · B).

Q: Find the Laplace transform of 0 2 (t – 6)² + 2 cos

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Q: T - 1 Y - 2 2-1 Suppose the symmetric equations of lines l1 and l2 are respectively. = 2 - y = z and…

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Q: Evaluate the integral +00 X3 dx. 1+ x2 0.

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Q: Show that ⊢ (x > 0) y = x + 1 (y > 1)

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Q: Example: A. Find the polar and exponential form of the following: 2. z = -1/2– V3/2i 3. z = -i

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Q: Use the above formula to write each of the following limits as an integral (a) 53 + n3 lim n00 j3=…

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Q: [B] Find the dual for the following linear programming problem: (i) Maximize Z = 3x + 4y + 5z…

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Q: you know f(t) = L¯'{F(s)}, how would you find {F(s)/s²j? %3D

A: Inverse Laplace transform

Q: Use the method of disks/rings to determine the volume of the solid obtained by rotating the triangle…

A: We will find equation of boundary lines of triangle and then shade the region . Then rotate region…

Q: Which of the following is not a vector space? (; :) A. The set of all 2x2 matrices of the form with…

A: Solution:-

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Q: 2. Find the Area bounded by the curve y = 4-x? and the x-axis. 3. Find the area of the loop of the…

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Q: 1. Find the determinant of the following: [2 0 1. 1 2 4 l4 4 2 0 41 -2 3 1 4. 4 5 -2 -3 4 5 2 61 2.…

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Q: X= (y-3)2 and X= 16 about the X=- 5

A: Given curves: x=y-32 and x=16 Revolved around: x=-5 To find: Volume of the object formed by the…

Q: The Fourier Integral Representation of f(t) is (0, t1 f(t) 1 [sin w + 1 -(cos w wt 1 [sin w + 1…

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Q: Express the integral as a limit of Riemann sums using right endpoints. Do not evaluate the limit. dx…

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Q: If m, n, p, q are integers, n > 0, q > 0, and r = m/n = p/q, prove that

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Q: 2. Find the volune og the solid gonned by revohing abaut thie lere y y=4x+1, y: -1 bounded by 4x +3,…

A: The volume for solid of revolution generated by revolving the area bounded by curves y=f(x) and…

Q: sin x P47. Let I = cos.x dx and J = J% sin x+cos dx, a e [0, ). sin x+cos x (a) By considering I+J…

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Q: SUseThe improved Methods SoNe the: dy x(i+メy)yc0)=3 h2o.て dx

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Q: b What is the general solution of the differential equation? Reason out why it is the general…

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Q: 3dx xV4-x²

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Q: Find the solution of the equation cos y dy? which tends to zero as x → 0o and has the value cos y…

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Q: Solve the nonhomogeneous opdr – 2rdo = q' In odo. equation

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Q: 1 1 1 8 27 64 11 29 65 125 1 4 9 16 1 1 1234

A: To find: Obtain the Lagrange interpolation formula from Vandermonde's determinant. Given determinant…

Q: 4. Refer to the IVP in Section 3.2 - Exercise 4 (previous page) Sketch the solution curves in the…

A: We can solve this using given information   Sketche

Q: +00 1 dx xln*(ex) 4 e

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Q: Find the absolute value of z: b. z= (2+ 3)/(3- 4)

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Q: Advanced Physics 3. Consider the discrete-time dynamical system on X = R, given by the iteration…

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Q: Determine the Laplace transforms of * 3, 0 12

A: We use the definition of Laplace transforms to answer this question. All that is required is to…

Q: Which of the following is true? 0. 1 0 O A. is a basis for M22. O B. is a basis for M22. 1 0. 0. 0.…

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Q: 1. Find the particular solution of the given equation, d'y dy +ty = 0 with y(0) = 1 and y (0) = 0…

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Q: 1.. The olation to y'tby'494=o is, 0)- The eolution to yl +94=5 G8wt will exhibits d) Jesononce when…

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

Q: Problem 2 A piece of string whose length is given below is cut into two pieces. One piece is used to…

A: Consider the length of the string which is used to make an equilateral triangle as x cm then the…

Q: a) Let q(t) = 4t2 + 2t + 9 be an element of P2. Write the coorfinate vector of q(t) relative to…

A: We have to find the followings ; (a) We have to find the coordinate vector of  q(t) = 4t2+2t+9 with…

Q: Which of the following is not a vector space?    A. The set of all 2x2 with integer entries and…

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Q: 1. Find the general solution of the linear differential equation using undetermined coefficients,…

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Q: Find a parametric representation of the solution set of the linear equation a +y+z=1 O =1+8+t, y= s,…

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Q: 1) [ x² y" – xy – 8y = 3x – Consider the DE 4 - - satisfy A) Verify that yı = x* and y2 = x the DE:…

A: The given ODE is x2y''-xy'-8y=3x-4x. (A) To verify:  y1(x)=x4, y2(x)=x-2 satisfy x2y''-xy'-8y=0. (B)…

Q: Use the Cayley-Hamilton theorem to find A', A', and A“ for the given matrix A. 2 1 - 3 - 3 -1 6 1…

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Q: Find the transition matrix from the ordered basis of 3 R? to the ordered basis of R?.

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Q: ĐUse the imProved wmethod Solve the: Sayt an x=Sinzt, yl0)=1 ,h20.

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Q: 1. 2– 2y + 2z = 3r – 2y + 2z = 3 2x – 3y – z = –72x – 3y – z = - 7 -x + 3y – 3z = –4-x+ 3y – 3z = –…

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Q: Determine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, –1, 0).

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Q: 172 lim n2 + nj + j² j=1

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Q: The Fourier transform of f(t) = te - -1<t<0 is otherwise O 1- jwe'+jw (- w+j)2 O 1+jwe'+jw (- w+j)2…

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Q: 5 3. Use partial fraction decomposition, linearity and s-shifting theorem to find the inverse…

A: To find the inverse laplace transform of given function H(s) first we will take the partial fraction…