Let g be an analytic funetion with g(-) # 0, g((-1) = -12, and g(*)(-i) = -36. If f) = then Res f(2)lz--i = O 2 O -2 O 3/2 None of these 6.

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A:

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A: To Show -

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A: Given f(x) is odd function.

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Q: 6. Determine all functions f analytic in |2|< 1 and satisfying ƒ(²-) = k+k² 1+k2' k = 2,3,4,...

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A:

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Q: Determine the z transforms of the sequences (a) {(-} (b)

A: Use the formulas below to obtain the Z-transform.

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Q: Q1(i) Prove that Lim + a+ 1 2n²+1 V2n²+2 V2n²+n]

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Q: 3 use the definition of latlace transforms to find £{+²H (E-5) } JINO

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Q: Let co be the space of all sequences of complex numbers that converge to 0, that is, co = {f: N → C:…

A: Let c0 be the space of all sequences of complex numbers that converge to 0. c0=f:ℕ→ℂ:limn→∞fn=0…

Q: 1. Find the first-order derives:

A: Given,      4x2+715x4+534x3-37x6+15x-30

Q: Find the field of quotients of integeral domain z[i] and z[√2]

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Q: Find the linearization L(x) of f(x) at x = a. f(x) = 3square root of x, a = 27 show all work

A: fx=3x, a=27 Differentiating with respect to x, we get f/x=3·12x    ∵dxdx=12x=32x Now,…

Q: Determine the z transforms of the sequences (a) {(-}}'} (b)

A: Z-transform: The Z-transform of a sequence is given by, Given:  a)  b)

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.