Evaluate, using Cauchy's integral formula: sin tz? + cos Tz? () dz where C is the circle |z| = 3 (z– 1)(z – 2) | cOS TTZ di) dz around a rectangle with vertices 2 + - 2+ 1 -1 .2 C

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A: The given series is, ∑n=1∞n!(-e)-3n. To find convergence by ratio test : limn→∞an+1an=L If L<1…

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Q: P2 Consider the two power series (3x)2n+1 f(x) = x + Σ (2n + 1)! n=0 (x + 1)" g(x) = 3n ln(n) n=2…

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Q: . Find the analytic function, whose real part is sin 2x/(cosh 2y- cos 2x).

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Q: (a) Find the radius of convergence of the power series 8 Σ(4" + 5") an. n=1

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Q: a b [2] ... c d 4 3 25 - [ 10 11 20 29

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Q: 5. a) Determine whether the given differential equation is exact. (sin. x)" dy 1+cos y = 0. dx

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Q: Solve all except 1

A: solution