Derive/prove following relations: a) (A x B) (C × D) = A· [B x (C x D)] = A• [(B. D)C - (B. C)D] (A. C) (B D) – (A D) (B C) |

Q: a²f af af and əx' əy :f(x, y) = (x+ y)(2x + y)² Compute se дхду

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Q: Find real numbers x and y such that iy 2 - i i + 3 1 + i ||

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Q: Find x, y e lº such that || x || ∞ = 1 = || y || = || x+y 2 || x #y.

A: As per the question we have to find two sequences x, y from the norm-space l∞ such that : ||x||∞ = 1…

Q: Premises: Vx(L(x) → H(x)) 3x (~ J(x) A L(x)) Conclusion: 3x (H(x) A - J(x))

A: Given that Premises:      ∀xLx→Hx                        ∃x~Jx A LxConclusion:  ∃xHx A ~Jx We have…

Q: Let f(x)=x2+8x+14. Find all values of c in the interval (−6,−2) such that f′(c)=0.

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Q: Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously f(x, y) = x2 − xy…

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Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: Show that the function f: R - {2} (arrow) f: R - {5} defined by f(x) = (5x+1)/(x-2) is a bijection.

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Q: Vx E X, (x, x) ¢ R. X = {1,2,3}, h of the following relations R on X is irreflexive?

A: Here given set   X={1,2,3}   we know that relation is irreflexive when each x belong X (x,x) dose…

Q: A f:X→Y where X,Y ∈ Z+ , and  0≤X ≤23 and, 0≤ Y≤59, X is hour of clock and Y is minute of digital…

A: Clearly the function is not well defined and neither 1-1. The function is not well defined as for…

Q: (Ri. - .) (Fj -X.):Zero prove thete

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Q: (a) Find x, y el such that x+y || x || .. = 1 = || y || = || ** ||**y. ∞o 2

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Q: 1 1. LET A= [x € r: x + 2] and B= [y € r: + ?]where r is the set of real numbers. given that f: A →…

A: Givenfx=x1-2x

Q: of af and Let f(x, y, A) = xy + A(5 – x – y). Find· ax' əy` af

A: f(x,y,λ)=xy+5λ-λx-λy .....(1) Differentiating (1) partially with respect to x, ∂f∂x=(1)y+0-λ-0…

Q: Prove that X∩(Y−Z)=(X∩Y)−(X∩Z)

A: We prove that X∩(Y−Z)=(X∩Y)−(X∩Z)

Q: evaluated at fo as follows. 1 0.5 0.2

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Q: Use the Runge-Kutta 4th order method to find the values of y where x is given that y = 1 when x = 0…

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Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

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Q: дz дz If z = x.f(xy), express x-y in its simplest form.

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Q: 10.30

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Q: Prove that f-(U B: -U(B.), %3D i=1 i=1 and n N (B.). 3=D1 i=1

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Q: L,x²(x³ + 8)²dx 19. Use the Fundamental Theorem of Calculus to evaluate:

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Q: - R-{-}→R-{} defined by f(x) = Show that f: R 3x-5 2x+1 is bijective.

A: Given function is f: ℝ - -12 → ℝ--32 such that f(x) = 3x-52x+1

Q: b) g(x) = S,* In(2r + 1)dr

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Q: Let x,y ∈ Rn Show that: |x + y| 2 + |x - y|2 = 2|x|2 + 2|y|2

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Q: Please help me prove this: Suppose x, y ∈ R. Prove that if 3x^3 + 21y = 3y^3+ 21x, then x = y or…

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Q: Find the linearization at x = a. f(x) = 9x*, a = 1 %3D (Use symbolic notation and fractions where…

A: We have to find the linearization of the given function.

Q: =   x ∈ R  1 ≤ x ≤ 1 +  1 i   =   1, 1 +

A: If x varies from -1 to 1 then x+1 varies from 0 to 2.

Q: Prove that f(x) = 5x? + 3x – 26 is 0(x²). %3D

A: Given: f(x) = 5x2 + 3x – 26  is  θ(x 2).

Q: 3. Let f(x) = { ,x<2 ax + b, x22 Find a and b so that f (2) exists.

A: To find the value of a and b

Q: Let f(x) = a2 +1, g(æ) = Va+3, h(x) = 4 (go(hof))+(gof) at x=2? %3D Find I-4

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Q: Using R, use antithetic variables to estimate the following: In(1+ x2) dt x2

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Q: If f(z) = 6tan(z) , then f'(r) = (A) In(6) 6tan(2) (B) sec2(z) 6tan(2) (C) In(6) sec2() 6tan(z) (D)…

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Q: Let fi = 1+x + x² + x³ , f2 = 1 + 2x + 3x? + 6x³, f3 = 3+2x + ? + 5x4, and g = 1+x + 2a? + tæ³. For…

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Q: Compute the discriminant D(x, y) of the function. f(x, y) = x³ + y4 - 6x-2y² + 2 (Express numbers in…

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Q: ху af If f(x,y) then is %3D x2+y ax

A: Given function,  fx,y=xyx2+y

Q: 5x+1 14. Prove that the function f: R \ {2} → R \ {5} defined by f(x) = is bijective. x-2

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Q: Let r (t)= - The x component of r' (-1) =

A: r'(t)=&lt;2t,3,5&gt; r'(-1)=&lt;-2,3,5&gt;

Q: 3x +1 III.(10) Prove that the function f: R – {5} –> R – {3} defined by f(x) = is a bijection. x- 5

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Q: Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously f(x, y) = 3x3 −…

A: A function's partial derivative z=f(x, y) can be determine by differentiating z with respect to…

Q: Prove that (X+Y) (X+Z) =X+YZ

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Q: Prove that ax² bx + (x − a) (x −b) (x −c) ¹ (x − b) (x − c) || x³ 3 (x-a)(x-b)(x-c) C +—+1 X-C

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Q: af Let f(x, y) = 3x – y4 + 1. Find of and əx ду

A: Given : fx,y = 3x-12y4+1

Q: Let R=[0,1]x[0,1]. xy3 dA= R.

A: Let's find.

Q: 2. If f(2) = e*, describe the images under f(2) of horizontal and vertical lines, i.e. what are the…

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Q: a) Let A = [-1, 1] = {x €R: -1<x< 1}. R = {(r, y) E A x A : ¤|+ |y| = 1 or |x| = |y|} %3D

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Q: The domain of the relation A is the set of all real numbers. Ay if |x-y| ≤ 2

A: Given relation is A=(x,y): x-y≤2, x,y∈ℝ Here x is the domain of the relation.

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.