Suppose n is an integer and z-z=r is a contour traversed once in counter clockwise , then P(z-z)" dz = 2 Ti if n= - 1 2 Ti if n= -2 2 Tti if n= - i 2 Ti if n= 1

Q: QUESTION 10 Suppose n is an integer and z-N=r is a contour traversed ple-,)* dz = once in counter…

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A: section formula for internal division  in vector form is OP→=nOP→+mOP→n+m According to the question,…

Q: Consider j1,ỹ2, ỹ,ER° and that ỹ,+y;+ÿ;=0. For Î=span{ÿ, ,ÿ and Y=span{ÿ2, ÿ}, show that Ý=Ỹ.

A: Given y1→, y2→, y3→∈ℝ5 such that y1→+y2→+y3→=0. Let Y^=spany1→,y2→ and Y~=spany2→,y3→. To show…

Q: ). Show that V - u -ly- tan' u < V - u 1- if 0<u<v, < tan 1+v? 1+u 4 2< tan 4 25 3 and deduce that 3…

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Q: A natural cubic spline is defined by Sa,(x-1)' +b,(x-1)² +c, (x - 1) + d, S(x) =- if 0sxs1 (x- 1)' +…

A: Step:-1 Since, we know for cubic spline S(x)=S0x=a0x3+b0x2+c0x3+d0…

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Q: ) Find the fomily of the equ ation of all lines in 3-space perpen diuler to 2x -y +2u u Given line

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Q: 1. Use the Intermediate Value Theorem to prove that the equation 3x - 4x? = 3 is solvable on the…

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Q: Prove d(x,y) = 8 if x does not equal y and 0 if x equals y is a metric on R, the real numbers.

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Q: Find the Fourir for fcae) = (1+x) [-x, ] %3D

A: Given function is fx=1+x and −π,π We have to find the Fourier series of fx. The Fourier series of fx…

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Q: an Prove that n! ell7. dz 2ni (Z)n+1 Where C is a circle 1Z| 3D1 %3!

A: We have to prove that ann!=12πi∫Ceazdzzn+1, where C is the circle z=1 Use theorem which is given…

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Q: QUESTION 12 Suppose n is an integer and z - z=r is a contour traversed once in counter clockwise ,…

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Q: Suppose n is an integer and z-z =r is a contour traversed once in counter clockwise, then dz = 2 Ti…

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Q: Juan said that the reason for #9 is ASA~. Why can't it be ASA~ and what is the correct answer?…

A: Please see the below picture for detailed solution.

Q: A, D, ai Ical Bis between A and C. If AB = 36, BC = 5x - 9, and AC = 54, find x. %3D %3D

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Q: Suppose n is an integer and z-z3D =r is a contour traversed n dz %3D once in counter clockwise, then…

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Q: Suppose n is an integer and z-z =r is a contour traversed once in counter clockwise , then n dz = 2…

A: Cauchy's integral formula can be stated as follows.

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Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

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Q: The area bounded by the curve y = 7x and the lines z= 2 and =9 above the z-aris is O 539.00 square…

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Q: ome 9/ for Find The domain Dp and Rag Re De fallowing fandinse,

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Q: Let C be the line segment connecting 0 to ni. Then ſ. 1- e2zdz = %3D a. 0 b. -0.5 + ni C. πί d. None…

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Q: If L is a line through 0 and if f is the orthogonal projection of y onto L, then || F|| gives the…

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Q: Find and when (TU – V)² In(W – UV) = In(2) at the point (T, U, V, W) = (1, 1, 2, 4).

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Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find…

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.

Q: If u, v are given unequal numbers anu (un-1+ Pn-1), vn = V (u –1 Vn-1), where n2 2 , %3D Un %3D 2…

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Q: If A %3D аx + За, and B %3D 5ax + 2а, — баz, find @AB- АВ

A: ANGLE BETWEEN TWO VECTOR

Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: Use the theorems and given information to show that r s. 12 3 4 87 6 5 44 = (13z - 4) ° , 48 = (9x +…

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Q: Suppose n is an integer and z-z=r is a contour traversed once in counter clockwise, then dz 2 Ti if…

A: Since it is the standard result which is true for n=-1 which proof is given in next step.

Q: ■ Show that the area of the triangle whose vertices are the [X1 У1 points (x₁, y₁), (X2, Y2) &(X3,…

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Q: If z=2e(i pi/20), use De Moivre's theorem to compute z5

A: Use demoivre theorem

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Q: I. Solve using De Moivre's Theorem. Given that z is not real number and z = 1, show that w = z-1 z+1

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Q: Ihow do you bnd the imit of as x approaches 0?

A: The limit of x+1-1x as x approaches to 0

Q: Suppose that A = SS−1, where  is a diagonalmatrix with diagonal elements λ1, λ2, . . . , λn. Show…

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Q: XE 2 Then 9 is, H-w Diso Disc 9:21 2 such That goo =zX, Sprove That. %3D 7. ctute

A: g:Z→Z such thatg(x)=2x For proving one-one/injective Let x1,x2∈Zg(x1)=g(x2)⇔2x1=2x2⇔x1=x2 So, g is…