4. Is M₂ (R) a field? Justify.

Q: 4. If [æf (x) + 2] dæ = x³ – a² then find the function f (x). 3 A) 2 3 B) 2+ C) 3- 2 E) 2– D) 3+ --…

A: The given equation is x∫x fx+2dx=x3-x2.

Q: 4. Let F = {s+t√2 s,te Q}. Show that F is a subfield of R. You may assume that √2&Q.

A: The objective of the question is to prove that the set F, defined as F = {s + t * sqrt(2) | s, t…

Q: Exercise 1. Suppose t₁ (n) = O(n²) and t₂(n) = O(n²). Encircle in the following list all the…

A:

Q: Exercise 6. Let f(x) = 2x-5logx. Then f(x) is а. О(х) b. O(x²) с. О(Зx?) d. All of these

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Q: 26. Let H(t) = 5+2e-t. Find the exact value of H-¹(9).

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Q: (6 y x - 2 y)d A R=[1, 4]×[0,3] 9 .A O 9 2 .B O 2 9.

A:

Q: 13) If it is known that -6 L{e% f(t}} s2 – 14s + 40 with certainty it can be assured that: a) f(t) =…

A: We will first find F(s) the using inverse Laplace we will find f(t) We know…

Q: Factor x4 1 completely in R[x] and then factor it completely in

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Q: 1 1 2 30. f(2x+4) = x x-3 ise f(2) = ? %3D -1 2 0

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Q: Q3: If P(X= x) = a 8(x) + b 8(x + 1); then a + b = A) 0.5 B) 0.3 C) 0.4 D) 1 E) None

A: Given: P(X=x)=aδ(x)+bδ(x+1)

Q: 2. Suppose that X = a →3. Prove that X = (ya) → (y →ß).

A:

Q: 11. Given /(r)-V1-2, fnd onctions /and g so that. /(r) (/o9)(r).

A: Here, we must express H(x) as a composition of two functions. This can be done in multiple ways. One…

Q: 1. Let f(x)=x² - x, xeR then f(f(f(v2))) is: -34 + V2. b. 2/2 +34. c. 34+2/2. d. 34– 2/2. e. 2/2 -…

A:

Q: 25. Which of the following is the answer for secx = V2 A. E + 2nk|k E Z}U {+ 2rnk|k € Z} 3 B. G+…

A: We will solve the problem

Q: Let F ____ {(a, b]: a, b E Q). Show that a(F) = B(R).

A:

Q: a(k) = eak coshw.k coshw, k ewok te-wok 2 eak coshw.k eak ewokteake-wok 2 X(Z) 3D글 z(enk e.k) + 글…

A:

Q: b) (i) Show that dz is a constant independent of z, and R. { Hint : z= Z, + Re"} 1 +- 2z-4 2 -z 3…

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Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

A:

Q: Prove that I(r + 1) = ar(r). 3. ii. Prove th at 3(m, n) = B(m + 1, n) + B(m, n+ 1). %3D

A: The required proofs are detailed below.

Q: 1) G T. 2) YSXA CAA AZA2 F K R E R

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Q: S 1.Prove that L (coswt): %| s2 +w2

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Q: [2 11 Q2) Assume A = |1 [3 4] 2 4 11 3 6 4 3 and B = show that (AB)' B' A'

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Q: Suppose that F(x)=f(g(x)) and g(14)-2, g(14)-5, f(14)-15, and f'(2) - 11. Find F(14). O 17 O 55 O…

A:

Q: (c) M=QPCR (d) N³ = 1

A: Given:Let  be tensors.Objective:Convert the expression  to tensor notation.Convert the expression…

Q: 2 16 v2 6. Prove that x V(2 – x) dr = 15

A:

Q: 95. Prove that ||v - w2 = ||v|2 + ||w|2 – 2v • w. 97. Prove that ||v + w|[² + |v – w|? = 2(||v||² +…

A: Note:- We’ll answer the 95th question since we answer only one question at a time. Please submit a…

Q: 6. so be it r = 3xi + yi – 2zk and f (r) : -- where |r| = r find all of grad(f) and div (-)

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Q: sv(8vh) (8→i)^(h→j) B. (i→j)→(fvh) .h Proof: Step Statements Reasons sv(gvh) (g i)^(h→j) gvh iv j…

A: We are given the following Logic: f∨(g∨h)             : Premise 1(g→i)∧(h→j)    : Premise…

Q: Prove that for any x > 0, y>0 (x² + y²) ³ ≥ (x³ + y²³) ³. Hint: Introduce a new variable z = (2)².

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Q: (3x)[R(x) V S(x)]→(3x)R(x) V (3x)S(x)

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Q: 12. Let f(z) =,h z 0. Then f(2 + h) – S(2) h A) – 4+ 2h 1 B)- 4+ 2h C)-- 4- 2h 4-2h

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Q: Simplify the Boolean expression F(x, y, z) = (x+ y) (x +z)

A: F(x,y,z)=(x+y').(x+z) simplify F(x,y,z)=x.x+xz+xy'+zy'

Q: 21. Let V1 = 1 0 -1 V2 H " V3 = 0 {V1, V2, V3} span R4? Why or why not? 1 0 0 . Does

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Q: Let f(x)= x+1, find all xeR such that f[f(x)]=2 the solution set is: а. у%3D0. b. y=x. с. у#х. d.…

A:

Q: Acollection of measurable sets is an algebra of sets.

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

Q: Find Lt Vx (Vx+c- Vx)

A: We have to solve the following limits, limx→∞xx+c-x