The Cauchy's formula for a Rectangle: Let Q be an open subset in C and f be a complex differentiable function on S Let RCQ be a closed rectangle. Then for any a € Rº, we have

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Q: max Z= 3x₁ + 2x₂ -X1 + X₂ ≤4 3x₁ + 2x₂ ≤ 125 X1 X₂ ≤3 X1, X₂ ≥ 0

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Q: 3Q. If z₁ = (cos50 – i sin 50), z₂ = (cos70 + i sin €) and z3 = (cos40 – i sin 40) then find 4 polar…

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Q: 1. Derive the Maclaurin and Taylor Series of the function below:

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Q: 5. Use transformations to sketch the function y=-3log10 (x-1) +2.

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Q: 9. F(x)= 4x¹-6x²+1 is even function True False оо

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Q: - Let A be the n x n matrix with all I's on the diagonal and all 0's above and below the diagonal.…

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Q: log3814 4log100-2 b) -log0.0135 d) 2log4128-5

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Q: Let S = { 1 - (-¹)" | n € N}. Determine inf S and sup S. Justify. n

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Q: 4. If ) (√4x) then x= B. C. 2 D. None of them

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Q: Q3. Prove by using logical equivalence method: (pr) V (q+r) = (p Aq) → r

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Q: 11. Determine the solution of Utt = u (x,0) = 0, u (0, t) = h, where h, k, and A are constants. c²ur…

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Q: y=-3log10 (x-1) +2 Parent Function y = log10x (x, y) VA Domain Range State the transformations…

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Q: that the function. 22²2² Bin 12 f(x) == x2 0 (x=0) of bounded variation on [1,1]. کر ۔ (x+0)

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Q: let W be vector that space and suppose USV SW are subspaces of W. Show that W N/u W ~ V/₁ defined…

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Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(8y) dy = 0,…

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