let A=(ai)nxx be symmetric and positive definite. Show that dii >o, i = 1, 2, ...

Q: Prove the absorption law of x + xy = x using other laws of identi

A: to prove x+xy=x x+xy=x1+y use the identity law x+0=xx·1=x hence,  x+xy=x·1+x·y

Q: 1 Prove that 3 dx s VI VI

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Q: Suppose that P(Xi = 1) =pi = 1-P(Xi = 0), i=1,2 If p1>=p2 , show that X1 >= X2.

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Q: Let A denote the 2 x 2 matrix We define a function (, ) : R² ×x R² → R by taking (x, y) = y" Ax, for…

A: We have A=1221. We are given the function ·, · : ℝ2×ℝ2→ℝ by taking x, y=yTAx, for each pair of x,…

Q: Evaluode Lim [x]+[2x ]+ n2

A: We know that, x-1<x≤x Therefore, 2x-1<2x≤2x ⇒3x-1<3x≤3x . . . ⇒nx-1<nx≤nx ∴ (x + 2x + 3x…

Q: (B1>0 (g) If a > b and c> d, then a + c > b + d. h) If a > b> 0 and c > d > 0, then ac > bd. i) If a…

A: For (f) ,We use a theorem that "if n∈ℤ and n≠0 then n2>0.

Q: (a) Use the first two digits as the stem. Then order the leaves. Provide a label that shows the…

A: The data is given on the winning scores of the conference championship games. Sample size (n)= 35

Q: 2. Show that In (- - ) = ( + 2nn)i where n = | .... .... ..

A: Consider the following expression: x=ln-12-32iex=-12-32icosx+isinx=-12-32i

Q: Find if y = tan- 5). Select one: A. 1-) В. 1+ (1 – 2)* C.d - 2 O D. I+ (1 - 1)* OE.+ (1-)

A: Given function is We know that derivative of tan inverse x is 1/1+x^2,so

Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

Q: Using DeMoran's thearem, show that: L (A + B)'(.4' + B')' = 0 b. A + A'B +.4'B' - 1

A: Concept: a. Given; A+B'(A'+B')'=0 We shall solve the Left hand side of equation. Apply Demorgan's…

Q: S # 3 X Use the fundamental Identities to simply the expression. 1) tan & coft 2) cos²0 2 +CSCO sint…

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Q: Evaluate p* sin 0 de dr.

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Q: Verify Stokes's Theorem for F = z²î + x²j + y?k and S is the surface z² = x2 + y2, y 2 0, and 0 szs…

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Q: Show dz 4 In= 는I미페 - for a<0. x <

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Q: +o0 - Find Ul-1/i, 1/i]- i=1

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Q: () - (" ;')-(,".) Show that: n+1

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Q: Show that is Reciz) e -ImZ p (ii) Im(iz) = Relz). %3D

A: Solution:- we have to show that  (1)    Re(iZ) = - ImZ (2)    Im(iZ) = Re(Z) where , Z = x + iy

Q: Soluti 03 16. A 11 22 1 Let Ax- b be a linear svstem of n eauations in n unknowns, and assume that A

A: Given: A = 03-2114225, b = 75-2  and Ax = b To find: The value of matrix x.

Q: Find sin a. (-/5 ,2) [ ?] 1

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Q: Ql Find se dx |

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Q: tan-1 3

A: tan-133

Q: For any natural number m, evaluate 1/m +x")( 3m 2m 2m +x 2x +3x" +6)"* dx, x > 0. m X

A: Topic:- Integration

Q: Determine the exact function value of cosh (In 2).

A: The given function is  Cosh(ln2)

Q: Differentiate, hcx) = In (x-Vr

A:

Q: Evaluate cosh(1+j)

A: We have to evaluatecosh(1+j)We know that

Q: (c) = y² %3D dr dy (d) y = sin x %3D

A:

Q: Determine 1-/[e-tt sin(2t)] 2- 23+3s)*

A: Given

Q: iv) z1 = et01 ,zZ2 = el®2 then z,.Z, = ei(8,-02).

A: Here, the given statement is wrong.