The Laplace inverse of L¯ is 6! O t6 6! 7! t7 7! S.

Q: Are the following two sets of coefficients orthogonal? -1, 0, 0, 1 -1, 1, 0, 0 Yes No

A: Given data is as follows: -1,0,0,1 -1,1,0,0 Yes the following sets of coefficients are orthogonal as…

Q: Find df (82 + 6y) dA where Dis depicted below. D Q

A:

Q: Show that

A: Given,  To prove 1  1    1a    b    c  a3      b3     c3=a-b(b-c)c-a(a+b+c)

Q: Find f"-1) if f3) = (3x + 1)° . %3D O a) 9 O b) -27 c) 36 O d) -9

A: Given function is f(x)=y = (3x+1)3  We have to find f'(-1)

Q: L[sih bt) 2.

A: From the definition of Laplace, L(f(t))=Fs=∫0∞fte-stdtSo,L(sin(bt))=∫0∞sin(bt)e-stdt Let,…

Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

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Q: Q2: Prove that: d csc-(InVx) dx -

A: The main objective is to prove ddxcsc-1lnx=-12xlnxlnx2-1. It is known that ddxcsc-1x=-1xx2-1.

Q: Problem 4 Let X, Y be subspaces of a vector space V. The sum X + Y is the set of all vectors of V…

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Q: Evaluate: S(4sin (x) – 3sec? (x)) dx

A: ∫ 4sinx-3sec2xdx=∫ 4sinxdx-∫ 3sec2xdx=-4cosx-3tanxAdd a constant to the solution=-4cosx-3tanx+C

Q: р T T F F F F 9 T T F F T F r T T F T Fill in all combinations of p, q, and r.

A: We are given truth table with missing truth values,So we have to fill the truth values for emty…

Q: dy Given a DE of dz 1-r-y using simple substitution, what must be your z? Ity Answer:

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Q: 6e dz by residue theorem, where C is the contour |2| = 2 Evaluate 524 + 25z

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Q: Use Newton’s Divided Difference Formula to interpolate f (1), if the polynomial has given points…

A: We have to interpolate f(1) using Newton's Divided Difference Formula.

Q: Z3+2, find |ZI.

A:

Q: 4. Explain how the following formula d (u₁-u₂-..- U₂) ² dx enable us to differentiate any…

A: The given formula is:ddxu1-u2-...-un=du1dx-du2dx-...-dundx. To Do:We have to explain how this…

Q: Calculate the triple product ā · (b x c), where ā =,b=, and č=.

A: Given vectors  a→=2 , -4 , 1b→=0 , 3 , -1c→=5 , -3 , 3

Q: What are the various applications of the dot product?

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Q: Find (a) v x w ,(b) w x v ,(c) w xw ,and (d) . v x v .

A: Solution:Given    v=-i+3j+2k              w=3i-2j-kFind:(a)v×w(b)w×v(c)w×w

Q: The center of D, is (Ro, R270}

A: THIS IS FALSE.

Q: Prove Equationally that A → BF¬B → ¬A.

A: let us check whether the given statement is true or not

Q: Find curl (2z i + 3x j+ 2y k). curl (2z i + 3x j+ 2y k) = )i + ( i )j + ( i i )k

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Q: Prove (A N (B U C) = Ā U (B U C) %3D

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Q: (e) [ - V TVT - 1 dr

A: to evaluate the integral.

Q: If F = ⟨F1, F2, F3⟩ what is div (curl(F))

A: F = ⟨F1, F2, F3⟩

Q: da J 5—4г — 2:а? 5 – 4x 2.x 2

A:

Q: Please explain properties or rules for each step

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Q: Find B so that BH B = A where A is from (1).

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Q: ry? Find I.A. -dA, R= [0, 4] × [ – 1, 1] г? + 1

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Q: с) V (и-у) - и х(Vху) - ух(Vxи)- (и-V)у+(ү-V)и %3D

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Q: projection

A: Consider the given vectors as, x=02y=11 This can also be written as, x→=0i^+2j^y→=i^+j^ The…