It gER[a,b] and if h(x)=q(x) except for a finite number of points in [ab],then prove that he R[ab] and a a

Q: Given f(x,y, z) = In(x² + y² + z²), show that ² f , ²f , ² f x² + y2 + z2

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Q: If TeZx Such that x is a momber of 27+5x-3=03 and S={x Such that x i. member of 2i+71+233/3 that T…

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Q: Q2/ fincd lachre trans form for at X- 3x+2X=lee

A: given equationx"-3x'+2x=1-e2tby assuming that initial condition is zero.x"=s2X(s)and x'=sX(s)and…

Q: Let x, y e Z. Prove that if 3x+7y is odd or 5x + 6y is even, then x or y is even.

A: We have given that for x,y belongs to integers. If 3x+7y is odd or 5x+6y is even then x or y is even…

Q: Find all numbers z such that Az3 + Bz² + Cz = D %3D B = [2 4 21 1 1 1. A = 1 3 1. 1 -2 2 4 21 C li 3…

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Q: Let x, y E R. Prove that if 21x + 35y = 45, then x and y are not both integers.

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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: • prove that y` = = for y= (of (1+x)) 1+x²

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Q: 1. Use the Intermediate Value Theorem to prove that the equation 3x - 4x? = 3 is solvable on the…

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Q: Prove that the function f:Q Q given byf(x) = 2x – 3 for all x E Q is bijection

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Q: ZW and ZX are supplementary and ZW and ZY are supplementary. Construct a proof that ZX = ZY.

A: <W  and < X  are supplementary angle  the sum of supplementary angles = 180 degree <W  and…

Q: Find the value of the Conj uction g(+) ifya know that w(f.g)=3e" and fCo=et (Wronskain)

A: We will find out the required value of g(t).

Q: I Find for each of the following. keving your anwer in terms of the parameter . 2r, y- 2

A: We have to find dydx for the following...

Q: S. Use the theorems and given information to show that r

A: The figure is as shown below : Given, ∠4 = (13x-4)o, ∠8 = (9x+16)o and x=5

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

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Q: is the gropt Q whch of Hhe of followring

A: Given that: 1. y=x2ex2. Graph of f(x)

Q: 2, 5x .3 b) Y = In 60(х, + + X, 2. 3.

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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: Show that the function f(z) = from [0, 0) to [0, ∞) has a fixed point c. Hint: Set f(r) = z and show…

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Q: T be the lineas translfomation et whose standasd matsine is A= 2 -2 2. - 2 Does T maps 3 3. R4 onto…

A: A=2-29203-230005

Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

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Q: 2 Let A B = -1 |0 and C = 7 Find x, y,z | 2 -3 such that AB =C.

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Q: If possible make an explicit bijection from [0, 1] to [-2, -∞. If no possible, Why? If…

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

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

Q: 1 1 b. From (i) prove that, xb + x ² + 1 + x² + x ² + 1 ² + 1 = 1 xa +x+b+1 c. From (ii) given in…

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Q: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

A: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

Q: c. Find all the points X1 x2 in R3 [x3. that are transformed to Explain.

A: Given, the transform spantial coordinates                               x1x2x3into plane coordinate…

Q: 1. Let A = {x E Z | 6 divides x} and B = {x € Z | 3 divides x}. Prove that A C B, and then prove…

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Q: Q3/A/ Prove that ) + ",) = C). %3D إضافة ملف

A: As per our guideline we are allowed to do 1 question at a time. I think you hav already done 2…

Q: Suppose that the functlons u and w are defined as follows. u (x) =x² +3 w (x) = /x+ 2 Find the…

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Q: Q2) If f(x) = (x), and g(x) = (2- x)i find (gof) (x) and the domain of (gof)(x).

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Q: Let x ∈ R. Prove that if x 0.

A: Given :

Q: find the root of the fnmetion ーX FCx)= ē^ _ x which lies betwen (o %3D

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Q: Prove that if X₁X and Ync, then (Xn, Yn) (X, c).

A: For a sequence of random variables X1, X2, X3,... to converge to a random variable X, we must have…

Q: Find the source Q cx) Such that the So lutiim Uckit) of + Q(x) 2 ə x² 0 < x <∞ | U(x,o) = 0

A: given equation ∂u∂t=k∂2u∂x2+Qx ,       -∞&lt;x&lt;∞            ...iux,0=0 claim- find the source Qx…

Q: Let r E Rt. Prove that if z – 2x2 +2 2021. -

A: Let x2=t, Now if x∈R+⇒t∈R+ ⇒t2-2t+2≤0⇒t-12+1≤0⇒t-12≤-1which is not possible for any value of t, for…

Q: Let x ∈ R. Prove that if x3 − x > 0 then x > −1.

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Q: Find the domain of gof, iff(x) =x² and g(x) = Vx-6. %3D O a.l-, - võJU(võ. x) O b. (-30, -6]U[6, ¤)…

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Q: What theorem shows that GTY = GUX? Osss O SAS O AAS O ASA

A: We have to check

Q: B a. In the figure, if AX = (3x + 1) cm, BX = 4x - 1 cm, AY = 4x + cm, YC= 5x-1 cm and x = 2, prove…

A: SOLUTION-

Q: By algebraic properties of R, prove that for every x, y € R with y # 0 (-x) y

A: We have to prove that by algebraic property that ∀x,y∈ℝ with y≠0 -xy=-xy

Q: B. Use indirect proof 1. Show that: Vx€z, if x2- 6x+ 5 is even, then x is odd.

A: Given : x2-6x+5 is even for all x∈ℤ   To prove : x is odd As x2-6x+5 is even . So,  x2-6x+5=2m for…

Q: I. Solve using De Moivre's Theorem. Given that z is not real number and z = 1, show that w = z-1 z+1

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Q: Suppose that fo sf,:X-gy and g,-3 YoZ Prove that (Hint : First use ce) to show that gfe g,, and then…

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Q: Let x, y e Z. Prove that if 3x + 7y is odd or 5x + 6y is even, then x or y is even.

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Q: 3 Q7- Let fw=ex-y, Find a fun ction y =gcW So that f. 9) (x) = X+ 2 .

A: Given f(x)=2x3-4 To find a function y = g(x) such that  (fog)(x)=x+2

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.