10. Find all the values of a in the interval [0, 27] such that f (a,=) - fxx (a,=) = 0 for f(x,y) = Sin x Cos y – Sin y Cos x а,

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Q: (b) Verify that the following function is harmonic u(x, y) = −e sin x - 2e-siny. Find a harmonic…

A: Here we have to verify that the function is harmonic and then find the harmonic conjugate.

Q: 4) Consider the function defined by 10) = /3 (sin (5 + *)) (증+0)) +4 V3 sin (+t) + 4+ V/3 (cos G…

A: we have to show that f(t) is a constant

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Q: 3. y" +y = 2 cos x - sin x; y = x sin x+ x cos x

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Q: Q1/: a: Using the relation showthat J-va (x) = 2 cos x

A: We have to solve given problem:

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Q: (a) Differentiate f(x) = Vx+4 by using the first principle. (b) Differentiate the following…

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Q: B) Find- for following functions: дz მა 1) z = exy tan y, x = s + 2t, y = s/t. 2) z = x² + xy + y²,…

A: The objective of the question is evaluate the partial derivative of the given functions.

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A: We will use basic formula of Integration for first one and from second part just Value of the…

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Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: Write the function f(x,y) = xcosh(x)cos(y) - ysinh(x)sin(y) + i(xsinh(x)sin(y) + ycosh(x)sin(y)) in…

A: f(z)=Re(z)cosh(Re(z))cos(Im(z))−Im(z)sinh(Re(z))sin(Im(z))+i(Re(z)sinh(Re(z))sin(Im(z))+Im(z)cosh(Re…

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A: We know thatddxtan-1x=11+x2

Q: Evaluate: f(cos 5x - 2 sin 3x) dx O sin 5x - cos 3x + C Osin 5x - cos 3x + C O sin 5x+cos 3x + C…

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Q: What is the domain of f(x)=Dsin1(IIn(x)l)? %3D Select one: O (0,e] O (0,00)

A: Given, fx =sin-1lnx  We have to find the domain of  fx =sin-1lnx

Q: e) s = cos (1– 21) -2 4t f) y = t+1, .2 x + x g) y =

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Q: What are the maximum and minimum values of f(x) = x + 2 cos x on the [0, π] interval

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