Let f(z) = E-oo Qn (2 – zo)" in the annulus 0 < |z – z0| < R. Give the definition of zo being a removable singularity.

Q: Consider A = {z E C : |2| < 1}. The complex line integral eiz dz laa z(z – 2) equals: (A) 0 (В) —ті…

A: Here we can use Cauchy integral formula to calculate the integral which states that if C is any…

Q: Exercise 13. Let f(z) = (z – 31) + 9)er. Evaluate fe f(2)dz, where C is Iz- 2i| = 2, positively…

A: To determine the correct options.

Q: 5. . Find sSSzdv where D is the 2 solid bounded by xty'tz=4 and 2= 13x²+ 3y2. (" sce Cueam Come')

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Q: Suppose f(z) is analytic in the unit disk D={|z| &lt; 1} and |f(z)|&lt;= 1 for |z| &lt;1, Prove that…

A: Assume that f(z) is analytic on the unit disk D ={z: |z| &lt; 1}.Also assume that |f(z)|≤1 for…

Q: a)show 6) Sop

A: a). It is known that, CovX,Y=EXY-EXEY... (1)EXY|X=X×EY|X...(2)EEX|Y=EX....(3) Now,…

Q: Evaluate both sides of divergence theorem for A = pa,+pcos(@)a , + za , through the closed surface…

A: Given vector field is  Divergence theorem

Q: Reduce Fredhelm Inlegral equahion the homogenous u(x) = a[K last) uce) dt where k(nst)=}…

A: To convert the fredholm equation u(x)=λ∫01K(x,t) u(t) dt to boundary value problem Rewrite the…

Q: Let o be the hypercube [0, 1]". For any f e C[0, 1] show that (). (x1 + x2 + + Xn dxjdx2 dxn = f ...…

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Q: Let f ={ (-6,4),(-5,3),(4,-6),(3,-5),(1,5),(2,6),(-3,5),(-8,2),(6,4)}  g=…

A: It is known that f-gx=f(x)-g(x) and f·gx=f(x)·g(x). The sets are provided as:…

Q: The number of zeros of sin() is: a) 1 b) Infinity c) 2 d) 4

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: a) let-1 ≤x≤ 1. Show that b) Using part (a), find En-1/ 1)", cos(x) c) Find The type of singularity…

A: (a)  Let  fx = x2  x ∈ -1, 1          Since fx = x2 is an even function so the Fourier series of fx…

Q: Find a formulaforvectorfield F= M(x,y)i+ N(x,y)j given the fact that for all points(x,y),Fpoints…

A: Any point, x,y in the two dimensional space can be defined by a position vector, v→=xi+yj .

Q: Let flup be differentia ble function f x & ys Satislyng df (9,0) = 2 f (,1) = 3 J E,): -3 dy f Co,0)…

A: Question: A function fx,y satisfies f0,0=1, ∂f∂x0,0=1,∂f∂y0,0=2,∂f∂x1,1=3,∂f∂y1,1=-3 Let st is…

Q: Given the multiple variable function f(x, y, z)= Ax*e» - Bz cosx*y°)+Cx*y*z?, where the coefficients…

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Q: 5 Thass [[1(², 3)dA = [² [² fff(x, 0 1 drdo

A: Given that the function fr,θ=4rcosθ+rsinθ. Find the value of given integral.          The formula…

Q: 6. Determine the number of zero's for h(z) = 2z* – 3z² + 2z – 5 inside the disk |z| = 2. (Use…

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Q: 4.) Verify the Divergence Theorem where F(x, y, z)=(x',xz,3z) given by x' + y +z² <4. and E is the…

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Q: 1) Solve the Laplace equation for the function f(x,y,z) = (ax+by+cz)^n, where n is a given positive…

A: Part (1):   Given that f(x, y, z) = (ax + by + c z )n   Where, n is a positive integer and a, b, c…

Q: c) Show that the image of the annulus {z: 1 -1 | W - 1²/31 | > /// } W = Z-1

A: To Show: The image of the annulus z : 1&lt;z&lt;2 under w=2z-1 is the domain w : Re w&gt;-1,…

Q: the exponents at the singular point x=2 (the roots of the indicial equation) for (x – 2)2(x + 1)y" +…

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Q: Q2: 2 xy"+y' +=y= x³ 3 X

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Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

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Q: Consider the I.V.P y'= y², y(0)= yo : a) find the interval of existence. b) For which y, the…

A: solution is given below...

Q: 1 (d) Last week, Amy walked a median of 7.5 kilometres each day. 1 kilometre = 0.6 miles The table…

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Q: 4. Find the isolates singularities of the following functions, and determine whether they are…

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Q: "Ct) + y'Ct) - 2 yct) = H Ct> y'co) = 6 where ond yro) = 0 t +1, # Ct) 2t 4う > 2

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Q: Consider the function f (z) = ²-sin z z3 The Laurent series of f (z) around 0 is : 1 z2 a) 3! 5! 7!…

A: Given: f(z)=z-sinzz3