Q3: Answer the following: a) Use Cauchy-Riemann equations to test whether f(z) is analytic. Here f(z)=(z) +i Re(z) - ez and z is a complex number. af(z) b) Check whether = 0 is equivalent to Cauchy-Riemann equations. az*

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A: Given that,  w = 32 lb Then, m = wg    = 3232 = 1⇒m = 1andk = w8   = 328 = 4⇒k =4

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A: From the above details we have,

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Q: (+²-16) 2) Suppose that 4,₁(4), 4, (+), 41(+) are solutions Of different ea. 4" - 34" + (Sin +34 +…

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Q: Q5-Show if the following series are converging or diverge 1) En=1 η10 2) Σ=1 (33) 1 3) En=14 Σ=1 n

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Q: resents direct dependencies om vertex i to vertex j. Arra forming topological sort to th

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A: Lets solve  the equation by Fixed point method

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A: Explanation of the answer is as follows

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A: Sol 1) ddxarccot1+x1-x=-11+x1-x2+1ddx1+x1-x=-11+x1-x2+1·21-x2=-1x2+1

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Q: Construct the Truth Table and determine if Tautology, Contradiction, or Contingency.

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A: From the above details we have,

Q: How to solve Lagrangian function

A: To find: the method of solving the Lagrangian function.

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Q: * The Geometric Series depends on what for ?convergence and divergence A) a O C) both a and r B) r O

A: I have given the answer in the next step. Hope you understand that

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Q: Drive the following function for :(y) 3(sin(2xy))²

A: We have to find the derivative .

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A: Given  X''(x)-pX(x)=0  , 0&lt;x&lt;1 …………………1 Boundary condition: X'(0)=-12X(0) , X'(1)=-X(1)

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Q: 4) Find a general Peal Solution of the equation 4" + 254 = 90e + + 2 C05(S+) + +8.2/5+ + sec (54)

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