If z1 and zą both satisfy z +z = 2 |z - 1| and arg (21– 2): then find Im (21 + z2). 4'

Q: By using the substitution u = 4x +1, evaluate (4x + 1) dx %3D

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Q: Residue of at z = -3 is (z+3)² Select one: a. -2 b. 2 C. 3 d. -1 е.

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Q: H.w Exl Let f(x)= 4x+2X+243and go)=3x+3x+3xx +4, where 2. t. f(x),900€75LX] Compute POX) +g (x).and…

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Q: 1-x 1 0 0x=x-7x denklemini sağlayan x değerlerini bulunuz. 21 -1 X 4

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Q: V7x+2-V6x+4 = )f(x مستمرة عند 2 = ۲ if x 2 and x # 2 1- قيمة الثابت الذي يجعل الداله (x-2) if x = 2

A: Continuous at x=2,  using rationalization

Q: 1 13 Compute: Lk=0 2k Compute: -1 k². %3D1 =D1

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Q: Compute divF and curlF for F = -r°(y – 2)i – (2² + y^)j+()k. 422

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Q: Let f(z) - 4z-1 pnd alz) - ar+b, where a pnd b are positive constants. If the composite

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Q: Q6: Sketch x(t) and find X(f) for t – T/2` ´t – 3T/2' an (2) - an() x(t) = A II + B II T T

A: Sketch x(t) using rectangular function.

Q: _1. Differentiate the following w.r.to x (i) V(x? + 1)3 .3,-2x (ii) + In (3x + 1)

A: Using derivative ,

Q: V(12r), v°(-8r)

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Q: a) If y = 3x – 2, x = 3t + 2, and t = 3k – 2, find b) Express y as a function of k ify = 2x + 5, x…

A: Introduction: A function is an expression, rule, or law in mathematics that defines a relationship…

Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: If y² - xy = 1₂ prove that: (2y-x)³ g -2=0,² is the second deravitive of y. Since y

A: The equation: y=f(x) can be differentiated with respect to x to calculate the equation of y'. The…

Q: Transform the following point, using the given rule: (-3,8) Rule: (x,y)-> (x-8, y+2)

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: Find x, y, z values according to x(i+j+k)+y(i-j+2k)+z(i+k)=2i+k

A: x(i+j+k)+y(i-j+2k)+z(i+k)=2i+k  =>(x+y+z)i+(x-y)j+(x+2y+z)k = 2i+k Now, comparing the…

Q: The domain of y = v2 – x is A. (-0,2] B. (-0,00) C. (-∞,2) D. [2,0) E. 0

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Q: (b) Compute 1₂ x + y √2 - 2² - y²|dA, = {(x, y) |x² + y² ≤ 1} D =

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Q: Find values of m so that the function y = e is a solution of 2y" +7y' – 4y = 0. TILE

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Q: Find d = gcd (270, 105) and hence find integers x , y such that d = 270x +105y .

A: GCD stands for greatest common divisor for two or more numbers.

Q: Prove that bx q = b. ((Vt) - Vt), where q = V x t

A: We have to prove b→×q→=b→·∇t→Tr-∇t→ for q→=∇×t→ b→×q→=b→×∇×t→          =b→×∑i^∂∂ti×t→…

Q: Write a in the form a=a+T+aNN at the given value of t without finding T and N. 4 r(t) = (41²) ₁ +…

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Q: F(f)= 2 x-3 4x+1 a Find the dom F and dom F b-) Find ran F and ran F'

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Q: Find | |- •√√√√ V 5x ry sin(x² + y2) dedy

A: ∫02π3∫05π3xysinx2+y2dxdy

Q: Given f(x, y) 90x + 80y - 2 – 4y? – xy, and evaluate f(8, 5). f(8, 5) = %3D

A: Given : fx , y = 90x + 80y - 2x2 - 4y2 - xy  To fine : f8 , 5 Solution : For value of fx , y , put x…

Q: Find an example for which (zc)d ≠ zcd with z ≠ 0.

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Q: Find xy2 √ R x2 1 x²+1 dA, R= [0,2] x [-4,4]

A: First, we need to identify the limits of integration. The rectangle R is defined by the vertices…

Q: Obtain an expression that solves for T,. To help with solving for T, you can use the linear…

A: we have σTs4≈σTs04+4σTs03Ts-Ts0   ...iσTs-ΓhA4≈σTs0-ΓhA4+4σTs-ΓhA3Ts-Ts0   ...ii simplify the…

Q: Write the following equation in the form w = u(x,y) + iv(x,y) h(z) = (3z + 2i) / (2z2 + 4)

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Q: 2. Let -2 3] 1 5 A = (a) Write down the quadratic form, Q(x), for AT A.

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Q: Write the following equation in the form w = u(x,y) + iv(x,y) h(z) = (3z + 2i) / (2z2 + 4)

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