2 Evaluate each of the following (1)f e 22 dz (2)S zsinz?dz (3) ; z2+1 dz z3+3z+2 -2z 3 Determine poles of the following function and residue at each pole z2 (z-1)(z-2)2 4 Evaluate sinz? dz eG-2) (z-) where C is |z|=1

Q: Which radical function has a domain of (xe Rx≤3) and range of (y e RIy2-4)? Oy--√x+3-4 Oy--√x+3+4…

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Q: (a) Find the constants A, B, C, and D that satisfy 1 1 1+ (w/o)² 1 + ((z-w)/7)2 Aw B Cw D 1+ (w/o)²…

A: Use partial fractions

Q: Using appropriate substitution, [sec (2x) – 1] tan(2x) dx is equal to

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Q: Determine the pole of the functions and residue at each pole for f(z) =Z2-2z (2²+4) (z+1)²

A: Step 1: Given the function f(z)=((z2+4)(z+1)2)(z2−2z)​ =>f(z)=(z+1)2)(z2+4)(z2−2z)​…

Q: 3. (b) Consider the function f(x, y) = a(x² + y²) + xy + 1 for some real number a. Find Vf. Find fxx…

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Q: Let f(r) = In r Find and simplify f"(x).

A: Please refer the attached image for complete solution. THANK YOU.

Q: 12 +3t-4 and 3t2-3 9.) Suppose that x = 3x 10

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Q: 3. Check for monotonicity for the following functions. TR = -20² + 14Q %3D TC = 20 + 10 100 AC = Q +…

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Q: 1. Differentiate the following. Simplify as far as possible. - 3.r)" + (1 – x)² – VF f(x) = V 2+

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Q: Set up integral(s) (DO NOT COMPUTE) which give(s) the volume when the region enclosed by y=1/x,…

A: Given that the region enclosed by y=1x, y=0, x=1 and x=3 is revolved about y=-1   To Set up the…

Q: When a mass of 2 kilograms is attached to a spring whose constant is 32 N/m, it comes to rest in the…

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Q: U = {X ER2x2 | AX=0}, OU= {XE R2x2 | XA=0}, == U = {X = R2×2 | A+ X = 0}, = {[18], [8], []} =…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Find the residue of the following functions: z3 i. f(z) : at z = 1,2,3. (z-1)(z-2)(z-3) 1 2 ii. f(z)…

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Q: .Let f, g andh are three functions defined as below : f: R>Rf(x) = 4x² – 4, - g. R→R8 (x) = V-5x+…

A: Given  f(x) = 4x2-4g(x) = -5x+1h(x) = 2x-5   a) fog(x) = f(g(x)) = f(-5x+1) = 4-5x+12-4 =…

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

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Q: nich of the following is a polynomial function? a. y = sin x b. y = cos x C. y = 3x d. y = x³

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Q: 4. Explain how the following formula d (u₁-u₂-..- U₂) ² dx enable us to differentiate any…

A: The given formula is:ddxu1-u2-...-un=du1dx-du2dx-...-dundx. To Do:We have to explain how this…

Q: 3. Determine the pole and the residue of 22+1 f(x) 24-z-2

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Q: Find the effect of each of the following operators on the corresponding function. Â = d2 A) f(x) =…

A: In #C d²/dy² , Perheps it will be d²/dx²

Q: Let y = sin(sin(50)). Then y" is equal to: %3D Q7 -25 cos (50) sin(cos(50)) – 25 sin(50)…

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Q: 3. Find f(t) given. 3 F (S) = 4(s+5) A. +3p St est C. 3 -5t D. I 4 eist

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Q: 2. In each case, write the function f(z) in the form f(z) = u(x, y) + iv(x, y): z² (a) f(z)=z³+z+1;…

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Q: determine if the functions are one to one y = √36-x², y = = = ² 2 y =√x+1 − 3 1

A: A mapping f: A→B is said to be one-one if for each pair of of distinct element of A, their f are…

Q: Find real numbers a,b,c,d such that And then find f'(z) =? f(x) = x² + axy + by² +1(cz² + day + y²).

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Q: Differentiate the following functions using product rule. 1. f (æ) = (3x – 9) (x – 6) 2. ƒ (x) = (æ³…

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx

Q: 6) Let f f(x)dx 16, f(x)dx 10, fdx 5 then f(x)dx = A)-1 C) 31 B)-11

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Q: What is the of y = (tan-¹4x)² ? 2 - 2tan ¹4 1+16x² 1 8tan ¹4x 1+16x² 2tan-1 ¹4x 1+16x² -1 8tan ¹4x…

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Q: O Consider the following function 5z2 – 4z + 3 f (2) = (z+1) (z+2) (z + 3) Find the residue at each…

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Q: Sketch the following functions -2. x² + y² + 2y + 1+ 2+ z = 0 -3. z² = x² - 4y² 4. z = -x² - y² - 1

A: We need to standardized equations to get type of surface they represent and then draw it

Q: 2 (x? - х- 6) R (x) X State the domain of the following function : 7(x? + 4 x – 21)

A: Given the function:       Rx=2x2-x-67x2+4x-21 Find the domain of R(x).

Q: A. Find the coefficients of the following derivative fi" = ci-fi-1+cifi + C₁+1fi+1

A: Given: Let consider the given function, fi''=ci-1 fi-1+ci fi +ci+1 fi+1 We have to find its…