(a) Find the constants A, B, C, and D that satisfy 1 1 1+ (w/o)² 1+((z-w)/7)² Aw B Cw D st: 1+ (w/o)² 1+ (w/o)² 1+((z − w)/T)² 1+((z-w)/T)² where A, B, C, and D may depend on z but not on w.

Q: For which value of x is A = x= 4 1 -4 4 0 0 1 NOT invertible? -3 r

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Q: For which value of x is A = x = 4 1 -4 4 0 -3 0 1 x NOT invertible?

A: The objective of this question is to find the value of x for which the given matrix A is not…

Q: A 3. Find (f g)(x) if f(x) = x2+x +1 and g(x) = x2 - x- 1. %3D %3D O (f 9)(x) = a4+ 2a + 3x? +2x +1…

A: We can find (f·g)(x) as below

Q: (a) 2+j - j(x+jy) メ=? y-? 1-j (b) (2+j)(3-j2) = a+jb a=? be? ((メ-j2y) -(y-Jx)-2) x? y?

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Q: d Calculate[r₁(t) r₂(t)] and 77[r₁(t) × r2(t)] first by differentiating dt dt the product directly…

A: Derivative of dot and cross product of two vector fields

Q: (a) Find the constants A, B, C, and D that satisfy 1 1 1+ (w/o)² 1 + ((z-w)/7)2 Aw B Cw D 1+ (w/o)²…

A: Use partial fractions

Q: A 1. What is (go f)(x) if f(x) = 2x + 3 and g(x) = ? %3D O (go )(z) = + %3D O (go f)(x) = + } %3D O…

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Q: 4 |(3t2 – 2t + 5) d

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Q: Find the L(e2" (1+ t)²). ,2t a) + (s-2)* 1 b) + (s-2)2 2 (s-2)3 (s-2)2 c)+2 (s+2)³ (s-2)? d) +…

A: The following formulas can be used to obtain the Laplace transform.…

Q: A [(0,6) U (7, 12)]n (2,9; B= A\({1,2, 4} U (3, 5)) and C = BU{11, 8}. Give an explicit and fully…

A: This is a problem of point-set topology.

Q: Let B = a = The function p(t) = 2 + 4(t − 5) + 7(t − 5)², can also be written as p(t) = a + b(t − 2)…

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Q: Show that A = has two different factorizations of the form A = L · U where L is lower triangular…

A: Given: A=0001. To show: A has two different factorization of the form A=L·U, where L is lower…

Q: Evaluate f (x + y - z)² dV for the box B with dimension: [0, 8] × [0, 7] × [0, 3]. B (Use symbolic…

A:

Q: x-ビ ere S70 and --xe g 00ー

A: Integrate: I=∫-∞∞exte-x-ts1+e-x-ts2dx Evaluate the integral using substitution.     The following…

Q: Let a bc A= d ef g hi Assuming that det(A) = – 7, find a) Det(2A) b) Det(A´') c) Det(3A') d)…

A: Given that: A=abcdefghiand det(A)=-7

Q: Compute 5f – 7g, given that f(r) - and g(z) - e. -1) "(z-1) Se

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Q: (8) IF: A=i+j+ k, B = i +2j - 3k Find A-B, A.B, 2A.3B, A.B, (A+B). (A-B)

A:

Q: Find the set of all values of a for which f(x) = x° +(a + 2)x² + 3ax + 5 is invertible.

A: We know that, for function to be invertible the discriminant of its first order derivative should be…

Q: 49

A: ln4te6t

Q: The residues of f(z) O-4/9,-4/9 O-4/9, 4/9 O 4/7,4/7 O 4/9,-4/9 O 4/9.4/9 4z (z − 1)(z + 2)²

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Q: 2j(5-j3) B) Given that (2a+jb)+(b-j3a)=- Obtain the values of a and b. (2+j)(1+j4)

A: Solve the left and right-hand side independently left-hand side 2ab+3ab+jb2-6a2 5ab+jb2-6a2…

Q: Find an example for which (zc)d ≠ zcd with z ≠ 0.

A:

Q: Which one of the following is isomorphic to Z4 x Z6/((2,4))?

A:

Q: Show that (AB)T and BTAT are equal.

A: Now,

Q: Prove that: ^ ( a ) 2 ² 1 ( ² + ²; ; ; ; ; x ² ) = ↓ sin¯' x } 3 + 2² (¹-²)=an (b) 1 ¹ tan^¹ x ܐ

A:

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

A: to evaluate the integral.

Q: 1) Find whether the signals are memoryless or memory? a) y(t) = 5x2(t+2) b) w(t) = (t-9)x(t)

A: a) Given signal is: yt=5x2t+2 Substitute: t=1. y1=5x21+2y1=5x23 So, the output at t=1 depends upon…

Q: Show that for constants a and b ‡ 0 (a) Mx+a(t) = eªt Mx (t); (b) Mbx (t) = Mx (bt); (c) Mx+a (t) =…

A: Solution-: We want to show that for constant a and b ≠0 (a) MX+a(t) =eat MX(t)  (b) MbX(t)=MX(bt)…

Q: Consider z1 = 1 - j2 and z2 = -2 + j3. Determine Im (21)?

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Q: dx In x +1+ Vx² + 2x| + C Vx2 + 2x

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Q: 2 In x 1 e* 2 1 In 2x -1

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Q: d d Calculate[r₁(t) r₂(t)] and [r1(t) × r₂(t)] first by differentiating dt dt the product directly…

A: give r1(t)=9ti+2t2j+6t3k and r2(t)=t4k So  r'1(t) =9i+4tj+18t2k and r'2(t)=4t3k

Q: Suppose (x1,x2) + (Y1,Y2) is defined to be (x1 + Y2 ,x2 + Y1). With the usual multiplication cx = (…

A: It is given that the addition is defined as x1, x2+y1, y2=x1+y2, x2+y1 and the multiplication is…