Let f(2)= =+2£o Z²-Z² a simple pole & obtain its residue. Evaluate بھی offlzidz with C endosing с Show that Z = Z₂ is both z=z₁ and Z=-7₁ $ (2+26) de z2-Z2 C

Q: Find the firct derivatioves of the follwing: - 3 ) y= 3x-x -2 4) y: Jerx 2) y: Ji-7x 5) y = 2メ-3

A: ddxxn=nxn-1 ddxu(x)v(x)=v(x)ddx(u(x))-u(x)ddx(v(x))v(x)2

Q: Let L be the line passing through the point P(1, 1, 1) with direction vector d=[2, 1, 0]T. Find the…

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Q: Let ū = (-1,2,4) and ū = (-3,5, 2). Compute the following: (a) ū+ū (b) .공 (c) ||해 (d) ũ - 7 (this is…

A: (a) Find u→+v→ as follows: u→+v→=-1,2,4+-3,5,2          =-1+-3,2+5,4+2          =-4,7,6

Q: Let →a=a→= and →b=b→=. Find kk so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).…

A: We Know that, Two vectors u and v are said to be orthogonal vectors if and only if u . v=0 Here, a =…

Q: 1. Find an orthogonal change of variables that eliminates the cross product terms in the quadratic…

A: Given Q=x12-4x1x2+x22

Q: Prove that ithe polynomial PCO =-2xP +2x2+loxx t6 has and fachor azero at M= 3, and fachm s ala the…

A: The given polynomial is px=-2x3+2x2+10x+6. It is given that x=3 is a root of the polynomial. If x=3…

Q: Define w := 1/2+√³,0 = -1/2 + √5, and 7 := " 1+5. Determine IQ[W,0,7](Q).

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Q: [t +3 If A = -1 6. t- 3 -6 one of the following must be true? 1 t+ 4] A) The rank is 3 ift#-4, B)…

A: Rank of the Matrix, and it's properties

Q: Show that day) = So, x** 0₁ X=Y. defines a metric on X₂

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Q: Let L be the line passing through the point P(-1, -3, -2) with direction vector d=[-1, 1, 1]T. Find…

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Q: a2u a2u 2y дхду a²u )Find du where ax - - axây' ay? u = x3 - 2x2 + 2y3 – 6xy + y ax2

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Q: 3 y`dy 3 (4 -у?): 2

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Q: Could you please explain this to me

A: Given, x = 20 degrees in the figure below

Q: Let v = (a) 27 t (5, 2, 5) and w= (1, 5, 0). - = 4w = (b) Let 3 (t, 1, 0). For which value(s) of t…

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Q: Find the midpoint of (6, 7) and (14, 11). O (7, 18) О 20, 18) О 10, 10) (10, 9)

A: given points :(x1,y1)=( 6,7)(x2,y2)=(14,11) Midpoint = x1+x22,y1+y22

Q: /0/#Thbox?projector=1 9) x+2 y- 6 z - 4 2u - 1 2v + 3 2w+ 2-? 1.2 хуz u v w-5 1-3 -2 -3 Compute the…

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Q: In the diagram below ABGH, BCFG and CDEF are squares. Prove that 21 + 2 = Z3. A В C D <4 <6 <5. <7…

A: GF/DF =1/√2 FD/FH=√2/2 = 1/√2 So, ∆GFD~ ∆ DFH Angle 1= angle 6

Q: line through the variable point A(k+1,2k) meets the lines 7x+y-16=0 ,5x-y-8=0,x-5y+8=0 at…

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Q: 25) Which notation describes the translation of the sailboat B(70, 20) to the lighthouse B'(10, 80)…

A: Given: B70,20, B'10,80 For reaching from point B to point B', we have to use operation x,y⇒x-60,…

Q: |-2+1 () 7:2 だ,て メ-ドコ X, +1メ」 メレ-3x, transformation is gi ven t of trensformation; 4) Show that it…

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Q: 5 - 25 + Z² = -1 2x + 34 = 2 -y-27 = 0 (Mabrices), find of 2 Rom Rescaling

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Q: 2. State the leading coefficient, degree, and symmetry. [K/U 6] b) y= e a) y=3x-4x² + 2 -6x c) d)…

A: Given: a) y=3x4-4x2+2Leading coefficient=3, degree=4 and symmetry=y-axis

Q: 2) Let T [ ] = DT [₁2 i] = i) 0 ii) 2T = 1 + (-c-d)x+ (-d)²x² + (a + c)³ x³. Then we have: -7 - =

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Q: Ifx.y,z are real numbers satisfying the equation 25(9x + y) +9:*–15(5xy + yz + 3:x)= 0 then prove…

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Q: ) find w=4 +iv if the function. in term of 2 is f(z) = (Z-32²) (2z+i)

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Q: Q2/ Find Hhe Parametric aned stendard.equatior of the Line Hhat passer through Ponts (-2,1,0)…

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Q: 3). B = (2 1 (5 1 and C = -3 :), find (a) Given that A = 7 3 -1. ЗА + 2B — С

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Q: If UW = 4t- 16 and UY = t + 14, find UY in rhombus VWXY.

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