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Q: HiW:By. ther Same. Way.find the ponel.seNies.ef..Cosix.

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Q: So æ[a + In(1/x)]³dx a= 7.5

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Q: Q5: Define nilpotent element. Are 1 and 3 nilpotent elements of Z9?

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Q: -4 c4x Evaluate . So S dydx.

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Q: If y(x) = In 5a4, find y'(x).

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Q: Evaluate 9x et3 dy

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A: Let us assume two matrices A and B. To prove or disprove if AB=I then BA=I. Let us consider matrices…

Q: O Find the Posifi ve value of * that işfie the egquation x-2X+ 452Bisection methed)

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Q: 2. Show that div r = 3 %3D

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Q: Prove that: sec a + sec(120° +a)sec(120° – a) = –3 sec 3a

A: To prove that  secα+sec(120∘+α)sec(120∘-α)=-3sec3α

Q: 1. By using the definition, show that

A: 1. (a) To show that,                            limn→∞4n2n+1=2

Q: Use z = a + bị to show that z + 7 = 2a and z - 7 = 2bi.

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Q: Prove that if x - Exp (A), then E (x²) = 2A².

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Q: Show that di = s> 0.

A: Laplace transform

Q: Make a conjecture for each scenario. Show your wor

A: Given that: Two odd numbers.

Q: 5) Let A= 18 Using Caley-Hamilton theorem find the expression A* -19A³ + 18A? + A + 21.

A: Please refer the attached image for complete solution.

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Q: = 4) Use the recursion formula Stan" xdx to calculate Stan³xdx tan" X n-1 n-1 -ftan”-2 xdx

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Q: 1. Do not use a theorem to find the ff. Z if yz? + z = 5xy – 1. %3D

A: In the multivariable function, if we have to find the partial derivative of one variable with…

Q: the (1,1)-entry of A¯1B?

A: (b) -8 is correct We have to find out the 1,1 entry of A-1B Matrix A and B is given where A=116118…

Q: show that x'-15x +C= O has at most root on E2,2] one

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Q: It is possible to regress x1 on y. a. True b. Falas

A: From the given dataset we have to check that , is it possible to regress X1 on Y1  or not.

Q: in tions Practice - Add Su 3. 3D 5.

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Q: In(z,) + In(-v3 – 1) = In(2) +i %3D

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Q: Зл. What is tanº 4

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Q: Find inverse of a mabrix by guan jordan mtel 3. 20 3. 230.

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Q: Find Soluton for up (:) -5 Il6) %3D given 一 -3

A: The given problem is to solve the matrix differential equation with the given initial condition, we…

Q: By Demoiver's theoren Find 2)

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Q: perform the indicated calculations [2, 1,2] + [2, 0, 1] in Z33

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Q: Show a Check for each. In othe 4) Find a. / (z + 4) dz

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: A= Find a portia lar soltPon of the syatem with

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A: Given integral is I=∫01∫y1cosxxdxdy

Q: 17) wheat is dhe ra dius of covegone corvegence 3"n! (x-4)" Given い= 5" (url)!

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Q: Prove that the expression 2y2 - 128 is equal to 2(x² + 2) (x² – 2) (x8 + 4x+ + 16) Swer:

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Q: Show that lam 2

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Q: 9. In OP, QR = 7x – 20 and TS = 3x. What is x? -

A: Joining QP and TP, we get the radius of the circle.

Q: ) Evaluate, using Cauchy formula C:2- (a) zz-l dz dz (6) ( e

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Q: 2. If Az? i| Find A 2. a A-l = I

A: Given: A=21-11 To find: A-1 Formula: If A=abcd, then A=ad-bc Formula: A=abcd, then A-1=d-b-ca.

Q: By 2 Cas X the Same. way prove that

A: Prove that J-12x=2πx cosx

Q: Express 3x, xπ, and xsin x using the base e.

A: Our Aim is to express the following function using the base e given below:-(i) 3x(ii) xπ(iii) xsin x

Q: 22. Use the adjoint of 1 -5 -1 A = 0. -2 1 to find A-

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Q: nd the supremum of each of the ecimal place.) , 12, 3} .2

A: Introduction: If there exists a real number M ∈R, called an upper bound of A, such that x∈ M for…

Q: 4. Show that: do Tb/(a? – b²) - a+bcos0 а b2 Where a>b>0 such that * -1+ 1. < 1 - a²

A: To Show: ∫0πdθa+bcosθ=πba2-b2 Concept: i. 1+tan2x=sec2xii. cos x=1-tan2x21+tan2x2iii.…