Prove Theorem| 2.3: (i) (A+ B)" = A" + B", (i) (A")" = A, (iii) (kA)" = kA".

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

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Q: EX/ show that im Cosy-1

A: Given limit is : limy→0cosy-1y To prove  limy→0cosy-1y=0 Use the trigonometry formula,…

Q: 2. Show that by using MEAN VALUE THEOREM . u-v < tan-1 v - tanu < if 1+v2 u-v 1+p2 0< u<v and ded…

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Q: Q2] Find the lower bound of Iz - 3|if |z - il < 1

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Q: Prove that I(e) = dr, e> 0.

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Q: Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

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Q: 5. prove thatS" erf (x) dx =o CA

A: ddx(erf(x)) =2 e-x2π   I =∫-aa erf(x) dxI= erf(x) x -∫ ddxerf(x) x dxI = x erf(x) -2π∫ x e-x2 dx-x2…

Q: Prove that v = In (x- 2)^2+(y-N)^2 is harmonic in every region does not include the point (2,N) and…

A: Given v=lnx-22+y-N2 where N=44. So, v=lnx-22+y-442                                    ........1 To…

Q: gorean Theorem. 12m 14m

A: Topic pythagoras Therorem

Q: 1 dæ using the residue theorem. (2² + 1)° Evaluate the improper intergal -00

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Q: Enter the function In standard form. y = 2(x-1)(x +5) The standard fom of y = 2(x-1)(x +5) is

A: y=2(x-1)(x+5) first multiply (x-1)(x+5) =&gt;(x-1)(x+5) =&gt;(x^2 +5x -x -5) =&gt;(x^2 +4x-5)

Q: prove using the IVT. √c +√c + 2 = 3 has a solution.

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Q: 3- Vn n=1

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Q: Use Fermat's Theorem in your proof that Vn E Z>², 2 is irrational. I

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Q: [2] Show that the functions f (x) = 4x" , and f,(x) = x*+* linearly independent (-00, 00). are on

A: To Show: Show that the functions f1x = 4xn, and f2x = xn+4 are linearly independent on -∞, ∞…

Q: followinp serves Dedermine is he conditionelly , I converye your work ond justify your absdlutely…

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Q: 1+ By using the definition In(1+x) = / 1 -dt, show that for a certain range of values of r, t…

A: Solution:

Q: Prove inf { ñt nEN}= %3D

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

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

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Q: 5. What is UF, where F = 0? Prove the correctness of your %3D answer / computation.

A: To find- What is ∪F, where F = ∅? Prove the correctness of your answer/computation.

Q: Vr+2+Vx-2 If a = prove that a -ax +1=0 Vx+2-Vx-2

A: To prove , we need to simplify the left hand side of the equation till it becomes 0. To do this…

Q: 3. Prove the pythagorean Theorem

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Q: どタ -e -at u Ct) = (a +jwjñ+!

A: To prove that tne-atut↔n!a+jwn+1 It is known that  ut=1 , t&gt;0=0, t&lt;0 Therefore,…

Q: (ii) Verify Cauchy-Goursat theorem for f(z) = 5 sin 2z if C is the square with vertices at 1土も-1土。

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Q: 0 40 0 0 0 0 40 0 Let S =0 0 0 4 0 Compute s for k = 2, ., 6. 0 0 0 0 4 0 0 0 0 0

A: We can solve this using formula of power of matrix

Q: ·[²₁₁-²² Compute (a) Trapezoidal rule de using the

A: Given integration is I=∫-11e-x2dx here f(x)=e-x2 For n=2 subinterval step size is h=1-(-1)2=22⇒h=1…

Q: 4. Evaluate the Kullback-Leibler divergence between two Gaussians p(x) = N(xu, E) and %3D q(x) =…

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Q: Prove that F(z) = 81 8z + 1 is chaotic on (-1,1).

A: To prove: Fx=8x4-8x2+1 is chaotic on -1,1. First plot graph of given function with -1,1 as follows:

Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: Which is the most famous theorem of pierre de fermat?

A: To tell which is the most famous theorem of Pierre de fermat

Q: Evaluate the integral.

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Q: Is 1z = 1 for all z ∈ C?

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Q: (2) If U = (1 – 2xy + y²)-³ prove that, x- = y?U® %3D

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

Q: ii) under z = x² - y² and above the square R = [1,3] x [-1,1]

A: Please see the below picture for detailed solution.

Q: 2. What is the largest possible c in (1) if X=R² and x₁=(1,0), x₂ = (0, 1)? If X = R³ and x₁ = (1,…

A: Given: c To find: a) X=R2b) X=R3

Q: 4.8. Show that Dirichlet's function 1, if x is a rational number, { otherwise f(x) = 0, is not of a…

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Q: 18. (2) = t"(-t)" dt, show that F(m). m! +1, n+1 %3D m and n are positive integers.

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Q: 4-5. Evaluate the Integral 31) dt

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Q: "(2) is also analytic, and hence its

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Q: prove using soundness that the converse of Axiom 2: (vx)A → A[x := t] is not a theorem

A: Solution: If Î" ` Ï• then Î" |= Ï•. Completeness If Î" |= Ï• then Î" ` Ï•. Thus, any formula proved…

Q: 1 1. S f(x) dt = Choose...

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

Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

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Q: lestion 25 Consider the following IVP: y" + 3y' + 2y = 12x?; y(0) = a, y'(0) = b

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Q: dv 4.)Prove that f -Incosv + Insinv + C sinvcosv

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Q: 1 If f(x, y,z)= of then x- y- 3z ду

A: Differentiate wrt y.

Q: 3. In class it was said that 'the chain rule is the most important rule within differential…

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Q: 5) Let z = f(x2 - y²). Show that y = 0 ду %3D ax

A: Here, ∂ represents the partial derivative, which means when differentiating with respect to x,…

Q: To test this null hypothesis, we compute t using a special case of the formula. state the formula?

A: In this case, we need to write the test statistic formula for testing the null hypothesis.

Q: Prove: |I| = 1. %3D

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