Consider ζn = exp(2π √ −1/n) ∈ C for n ∈ N. (c) FIND Aut(Q(ζn)/Q) and JUSTIFY your answer.

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y * logy x *

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Q: 6. Find all the values of z satisfying sinh z = = -j1.

A: What is Hyperbolic Function: The hyperbolic functions in mathematics are comparable to the…

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Q: Q1: - Use N.R.S. Method to solve the equation f(x) = e-* - cos x start %3D with x0 = 1 and use four…

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Q: Suppose that Mdx + Ndy 0 is an exact equation, and M and N are both homogenous functions of degree n…

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Q: b) Suppose x # 2. Find dif dx In y = In (x - 2)² √x² +1

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. ƒ(x) has a root in [0,1]. If we…

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Q: (x²-cos(2x). c. T(x) = x d. T(x) x2. find Q at x = t/4. = 100e-3x + In(4x), k=470, A= 0.01r and x=…

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Q: 16. Find the root of f(x) = x³ – 2x2 – 2 = 0 in [2, 3] correct to 3 decimal places, using the…

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Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O11x

A: Given: lncosh(11x-sinh(11x)) We know that   cosh(x)=ex+e-x2        sinh(x)=ex-e-x2   Then…

Q: Find the least order for homogen D. E. with constant coefficient which has the solution : 6.x3 +…

A: The nature of roots is given as:Corresponding part of C.F.Nature of roots of auxiliary equation1One…

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Q: 1. Evaluate the integral |(x² - 5)e*dx 8.

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Q: What is the maximum value of y = cos(0) for values of 0 between -720° and 720? O A. -1 О в 1 O C.0…

A: Given that: y=cosθ     and θ between -720° and 720°

Q: 2) Give a big-Oh estimate, O(x³), for the function f(x) = (1 + 2x + 2cosx + 2r*)(log x² + 3lx| + sin…

A: 2 Given function is fx=1+2x+2cosx+2x2logx2+3x+sinx+cosx. We have to estimate Ox3 and determine the…

Q: .2 -dædy In (x) ey

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Q: sin x – e-* = 0, [0,1]

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Q: Use the Beta and gamma function -1 n! 1- Prove that x™(ln x)"dx (m+1)n+1

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y logy x * * -

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Q: Suppose that Mdx + Ndy 0 is an exact equation, and M and N are both homogenous functions of degree n…

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Q: Test the ff ODE for exactness and find the general solution of the DE. (2x + 3y) dx + (3x + 4y) dy –…

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Q: hD (Hint: E =eD and Sinh x: 2 Q3: Prove that 8 = 2Sinh %3D

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Q: 1. Suggest ways to avoid loss of significance in these calculations. (a) √√x4+4-2 (b) ln(x+√x² +1)…

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y * logy x |

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Q: Find y' (y prime) and y" (double prime)y = cos(x2)

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A: Please rate and feel free to ask any query about any part.

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ(x) has a root in [o,]. If we…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the different…

A: The annihilator of xn-1 is Dn The annihilator of xn-1sin βx is D2+β2n Now the given function is…

Q: Find the solution to the initial value problem for f(x) = 0 and g(x) = 5 sin 3x. q². - 00 0, u(x,0)…

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Q: . Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. f (x) has a root in [0]. If we…

A: Newton-Raphson iteration scheme is given by  xn+1=xn-f(xn)f'(xn) We use this formula to estimate…

Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O 11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O…

A: In this we have evaluate the equation ln(cosh(11x)-sinh(11x)).

Q: Consider the function f(x) = cos x - 3x +1. Since f(0)ƒ () <0, f(x) has a root in [0]. If we use…

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Q: Find a root for f(x) = xcos(x) + e* + 2x using the Newton-Raphson second method.

A: The Newton's iteration formula to find the root of function y = f(x) is:  xn+1=xn-f(xn)f'(xn).…

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Q: 2. Prove that g(x) = sinh x + x – 1 has a zero in [0, ln 2].

A: To prove that gx=sinh x+x-1 has a zero in 0, ln 2.

Q: The definite integral from 0 to = of cos x sin xesin² x dx is 4 O e - 1 e+1 e-1

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Q: prove using the IVT. e^x + ln x = 0 has a solution.

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Q: Find 뿐 for the ry – ln(xy) = 1 0 뽈 ㅇ-볼 O 래 ㅇ-픕 following:

A: The given expression is xy-lnxy=1 we have to find dydx use the derivative formulas, ddxx=1…

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)? dx y logy x

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