The multiplicative inverse of x+ x+1 in Z2[x]/< x* +1> is: X^4 x^3 None X+1

Q: Find the fourier expansion for the function whose definition - - <x <- 2 x, - 2 (x) 0, <x< 2 2

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Q: The inverse of 3 - - 4 x + 1 g (x) = | is . ... 3 + 1 x – 4 –1 g (x) = 3 -1 g (x) x + 4 g' (x) = 3…

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Q: Find inverse Z-transform 1+- X(z) = (1 - -)*

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Q: (22-4) (교3-4z)3 dz

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Q: rivial of

A: To find the non trivial of Z8 as,

Q: 6 -2 1 |-4 1 -1 l1 0 1

A: We have to find the inverse of matrix using Gauss jordan method.

Q: The inverse of 4 - 3 X – 2 k(x) - is ... 4 + 2 x + 3 k- (x) k- (x) = 4 (x + 3) + 2 %| k-' (x) = 3 4…

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Q: Show that, cosh-1 x = In (x + /x² – 1)|

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Q: Prove that (csc"x] = d -1 2 XVr - 1

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Q: -25 Evaluate the integral: dax x²Vx2 +25

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Q: Differentiate y O 1 4x +2 = x(x-1) (2x²(x + 1)) 3(x-1)²(x²+2x+1) 8x² + x 2 2 O3(x-1)² (3x²-1) 8(x² +…

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Q: Determine whether x^5 + 2x^2 + 1 is reducible over Z13

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Q: problem in photo attached

A: Take the constant out of the integral sign. Simplify the expression  as x1/3

Q: Evaluate the integral. 6 1 (x² - 1)3/2 2 (x²

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Q: Evaluate this indefinite integral: 6x^5dx-18x^2+7

A: We have integrand fx=6x5-18x2+7 We have to evaluate  ∫6x5-18x2+7 dx We can write as ∫6x5-18x2+7…

Q: mial x3+2x+3 EZŞ[x] product of irreducible polynomials of 75[x]- e se

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Q: 5 x²ỹ+ 3xỹ + 5y = In (x)

A: Solution

Q: Evaluate the integral of 1/(x3-1)

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Q: Use any method to evaluate the integral. 4 - 4-X xp- 4X + 4-X

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Q: Evaluate the integral. 9. 1 dt - 9

A: Consider the integral: substituting and solving

Q: The multiplicative inverse of x2+x in Z2[x]/ is: None x^4 X+1 x^3

A: we have to use the definition of multiplicative inverse .

Q: Divide f (x) = 2x ^ 4 + 3x ^ 2 + 10 by g (x) = 3x ^ 2 + 5x + 1 in Z11.

A: Solution:         To Divide f(x)=2x4+3x2+10  by g(x)=3x2+5x+1…

Q: xp- x2 +9

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Q: Evaluate the integral: Sen(1²2+3x-7) е dx A x² + 5x+In 3x-6|+C XZ B +5x+31n|x-2|+C 2 C x ²2+ = +…

A: On solving this we will get

Q: Evaluate the definite integral. S x3Vx² + 4dx

A: A definite integral is an integral  with upper and lower limits. It is restricted to lie on the real…

Q: The integral 15x* - x* - 43x – 19 (x + 1)2(x2 – 6x + 13) can be rewritten as

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Q: Find the number of positive integers less than 1000 that can be expressed as the difference of two…

A: Find the number of positive integers less than 1000 that can be expressed as the difference of two…

Q: Determine whether yy00 ory-y – ∞ as x-7-a∞ Ond x-7∞, 2 =x=-4x²-4x-8

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Q: c) : Evaluate the integral xp- x2-4x-5

A: Given ∫xx2-4x-5dx

Q: Find the integral of f(3x2 + 4x + 1)*(3x + 2)

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Q: Find the Fourier integral foxx) 5 if -25X TO -8 iP xx2

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Q: 3. Evaluate the improper integras: -0.5x +5+5 (a)

A: Part(a) Given:  Evaluate the improper integral.

Q: Find another representation in which '(2;)" a. ris negative and o<e < 2n b. ris positive and -2n < 0…

A: The point is r, θ=2, π3

Q: Evaluate the integral [5x/( x²+1)(2x-2).

A: Given, the integral

Q: it is unbaised estimated of a Then Show That ta is baised estimated of 02. Theorem:- if

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Q: Show that 1 sech-1x = In x2

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Q: 13 1 (1+2x)?

A: We have to integrate the given integral

Q: The integral x²/4 - x²dx can be determined using the substitution 4- x2 = t.

A: Given integral: ∫02x24-x2dx

Q: Evaluate the integra 4 X - 5 /1

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Q: How do you solve for the inverse of of each element of ℤ7 with respect to ×7?

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Q: Verify that Jp+1(x) + 2/½(x) –- Jp-1(x) = 0

A: Verify that, Jp+1x+2Jp'x-Jp-1x=0 The Bessel's function Jpx is defined as follows, Jpx=∑n=0∞ -1n…

Q: Show that0+0iis a ‘complex additive identity element’; andthat1+0iis a ‘complex multiplicative…

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Q: The multiplicative inverse of 1 + 3x in Z,[x] is: 4x+1 6x+1

A: We can see only first two options in the given picture. And these two options are not correct.

Q: xif 0 1 Tif if

A: We have to solve given problems:

Q: 3,80lVe this equadioR by USE GalSian eli minalion- X-34+ 42 =1 2W-2X +f-1 2W -X -27 + 47=0…

A: Given system of equations:x-3y+4z=12w-2x+y=-12w-x-2y+4z=0-6w+4x+3y-8z=1To find: values of w, x, y…

Q: Express x8. -x over Q[æ] and over F2[x] as a product of irreducible

A: Let f(x) = x8 — x. Over Q,f(x) = x(x7 — 1) = xϕ1xϕ7x=xx-11+x+...+x6 Note that  ϕ1x and ϕ7x are…

Q: Use syntheti¿ division to firid fiz) in f(x) = -x+5x²-7x+1

A: We have to find function value

Q: ( - 2ry + 6z) dz - (2 - 2ry + 2) dy

A: