result by induction. 88. Prove that d2n d2n (cos x) (1)" sin x dr2n (sin x)= and (-1)" cos x. dr2n

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A: The required results are as follows: cos2 x=12+12·cos(2x) and cos 2x=1-(2x)22!+(2x)44!-(2x)66!+...…

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Q: Q.3- Prove that: 2n 1 (cos =0 +i sin-) + 10 2cosne eino

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Q: 0 Prove for every x in the interval (0,1) the following inequality holds x² + sin² (ro) √T 1 + cos²…

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A: We are authorised to solve only one question, please repost remaining questions. Indefinite…

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Q: 7 Use the Intermediate Value Theorem and Rolle's Theorem to show that the equation 2 = sin z+1 has a…

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Q: gent subsequer O an = (-2)" O an = 1+ (-1)" · 10(-1)"-n n sin () %3D O an = O an = 1+2· (-1)"

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Q: • 8 If In = 7/2 e*cos" x dx, where n 2 2, prove that: %3D (a) In = 1-n[" /2 e-* sin x. cos"-1 x dx…

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Q: D n In (1+ n=1 n16 arctan E 5" In (1+ > sin n=1 2n+1 n=1 F

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Q: Express T(x)sin x-root(3)cos x into the form of T(x)=Asin(x+theta) , where A>0

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Q: 2- Exercise: Evaluate a) L{4x? – 3 cos(2x) +5e*} b) L{4+sin (x) – e**}

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Q: 1 Find Maclaurin polynomial P, to ƒ (x )= 1 1 sin Ax cosx 1-x 1+x

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Q: (a) Find all the solutions of cosh z = 4 (Hint: cosh z =

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Q: 5 find aroot of the eqution f(x)=x²-4 Sinx = 0 using the 2 Newton-Raphson, Xo = 3,6=0.0005

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Q: (d) Show that there is some x with 0 < x < 2 such that x2 + cos(ax) = 4. %3D

A: Solution-