(a, o) is not measurable. ylgn ihi

Q: x+y uis = 1 n upi = no • prove that x-+ y-

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Q: Find the value of c such that S xe = 3.

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Q: Given f(z, y) = et y" - 2°y, show that fry = fyx-

A: Partial differentiation

Q: Let fr)-ll for x0, then/(x) is Selact one A-1 * CNone of these DNot defined E1 a.

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Q: Give an e xam Ple of (T, m') ameasurable SPa ce F; x → T {E & CX : fCE) ET3 m is not

A: Given, Τ, m a mesurable space fi:X→Τ , m=E⊆X: f(E)∈Τm is not a σ-algebra on X.

Q: y If z = show that = 0. x + y?*

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Q: Show that (A − B )T = AT − B T .

A: Given  (A − B )T = AT − B T

Q: a) What is the dimension of {(x, y) E R² : x + y = 0}?

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Q: Find the d. c. of T from definition.

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Q: Let z = ety, where x = Vuv and y . Find dz in terms of u and v.

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Q: For z C, show that the solutions of cosh(z) = 1 are z= i2km, for ke Z.

A: We need to prove that the solutions of the equation: cosh(z)=1 are z=i2kπ, where z∈ℂ, k∈ℤ.

Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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Q: Given F(x, y, z) = (z, x, y) Solve for: а) divF b) curlF

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Q: If f = xi+ yj+ zk,1Fl =r,and n =, then show that grad (E) == %3D

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

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Q: Discuss the cosets of { (x, y) | x, y E R, x = y } in (R × R, +).

A: {(x,y) / x,y∈ℝ , x=y} in (ℝ×ℝ,+)

Q: defined BCX,x). a norm Dn

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Q: O prove that : (2) DO 2x e dx a e +b where a, b >o

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Q: if x? + y? = 4 then prove that = d'y dx %3D

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Q: what will be the valid conclusion for the given hypothesis: "f U is the midpoint of HT Then HU TU…

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

Q: x is the distance 1:- Show that the from morm Il x|l o7 2 to

A: We have to show that x of x is the distance from x to 0 Hence, x can e written as x−0 x=x−0 The…

Q: limf, is measurable 00 ylan ihi

A: GIVEN a statement

Q: en Gx) show that GCxx) = to is a t Slution to x y" + Cy')a = c

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Q: For which values of z is w =1/(z – i), defined? For these values obtain u and v and evaluate w when…

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Q: b) y= In( see x)

A: Answer and explanation is given below..

Q: Z = X, + X, + at X1, X2. are NC

A: We are given,  X1, X2... are independent random variables with E Xn=mn  and N∈P0(λ). The set is…

Q: b) = f ) then prove that x ux + y uy + z uz = 0 u

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Q: prove that 16 x (I+x) dx 306

A: The product rule of integration states that∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx.

Q: Given f(z, y) = =* y – z'f, show that fry = fyx-

A: See the attachment

Q: Find k so that dx = ke" + C.

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Q: If S e-t)rLnt dt, Find the valae of (n)

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Q: For x, y E [0, 1], prove that 1 xy(1 – x – y) < 27

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Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x 1+ x²

A: Answer is mentioned below

Q: f(z) =e? is contiuous in C

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Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

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Q: If E?uz = x² and h = 1, then find ux. %3D

A: The objective is to find ux. Given information is: E2ux=x2, and h=1.

Q: Iff, g e R(x) on [a, b), prove that f? dx + g? dx 2 2 Ifg | dx.

A: Given that, f, g∈Rx on [a, b]We need to prove that∫abf2dx+∫abg2dx≥2∫ab|fg|dx

Q: f(z) = e? is contiuous in C

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Q: a²z If z = arctan ), find ( ay?

A: Given,           z=arctanyx= tan-1yxTo find           ∂2z∂x2+∂2z∂y2=?

Q: Solve the following Bernoulli DE's. *+ x*y = x®y? a) b) y' - = y %3D

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Q: Use the properties of E(X) to prove that E(aX +b) = a E(X) + b.

A: For a random variable X, the expectation of X is defined as E(X).

Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x , 1+x²

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Q: (a, b) is measurable. صواب ihi

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Q: Q/ z = x + f(a) and a = ry. Show that: 尝-端=

A: We use the definition of partial derivatives to prove the given result.

Q: If p(x, y, z) = x²z + ey/x, evaluate grad op at the point (1, 0, -1).

A: The function is φ(x, y, z)=x2z+ey/x

Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Statements and Logic

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