(iii) af A function is analytic if = 0. Prove that f(x, y) = az x-1-ty (x-1)²+y² is analytic.

Q: The functions f₁(x) = x² and f(x)=x³ are orthogonal on the interval [-3,3] ? True False

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Q: he absolute extrema of J(*) = ,2+2x +9 n(-1,5]. %3D

A: The given function is  f(x)=xx2+2x+9 on [-1,5]

Q: If  f′(x) < 0 for 1 <x< 6, then f is decrescent over(1,6) True or false and why

A: If  f′(x) &lt; 0 for 1 &lt;x&lt; 6, then f is decrescent over (1,6) True or false and why

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: √x² + y² x-1 (a) Find and sketch the domain of f (x, y). 2. Consider the function f (x, y) = 4 (b)…

A: The given function is  f(x,y)= x2 +y2-4x-1 We know that the domain of a function is the set of…

Q: Examine whether the following function is Analytic or not ¹() (z) = ln(x² + y²) + i tan-¹

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Q: IfY C X, show that inf (X) < inf (Y)

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Q: 27. dy dt dy -y², y(0) = 1/2 28. =t²y³, y(0) = -1 dy dt dy

A: We have to solve given differential equations.

Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

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Q: Let f(x) = 8 - x f-¹(x)

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Q: Does f(x) =x3 -1 on [-1,1] satisfy the conditions of Rolle's the Rolle's Theorem. Justify your…

A: Rolle’s Theorem: If a real valued function f(x) (i) is continuous on [a, b] (ii) is differentiable…

Q: 2. Sketch the domain of the following functions: a) f(x, y) = b) f(x, y, z)= 2-x-y - eª %2 In(4-x² -…

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Q: a) f(x,y) = x³ + y³ + y(3x²y+ 3ry²) b) f(x,y) = x² + iy³

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Q: Let f(x, y) = √√/175 – 3x² – 4y² Evaluate f(1,4)

A: Given :To Find :

Q: u+iv is analytic function, under what condition (if any) v+iu

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Q: Discuss the analyticity of  f(z) = Re(z 3)   Find whether the given function is analytic or not.…

A: A complex valued complex variable function is analytics at z0 if it is differentiable every point in…

Q: Sketch the graphs of the function f(x) = sin x .

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Q: If f is a function defined from R to R, is given by f(x) = 5x - 3 then f -(x) is given by %3D -- 20…

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Q: Show that f(x) = 1/(1+x) is analytic on (-1, ∞).

A: To show that f(x) = 1/(1+x) is analytic on (-1, ∞), we need to show that f(x) has derivatives of all…

Q: Find where f(x) = 1-ax x(x-a)(x+b) is discontinuous.

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Q: Show that the function f(x)=√x+1 is differentiable in 2 = 2 but not differentiable in x = −1.

A: Given data:- The given function is, fx=x+1

Q: f:[0,1] -> [0,1] such that f(x)=x^2 has two fixed points. Is this true?

A: Given that f:[0,1] to [0,1].

Q: Determine the point at which the function is not analytic iz² – 2z ƒ(z) = 3z + 1 - i

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Q: Determine whether the function f : R\{2} –>R\{0}, defined by f(x)=(1/(x-2)) is bijective or not.

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Q: 2. Consider the function f(x) = e¯x -x5-x7 (a) Use the Intermediate Value Theorem to show that there…

A: We first recall definition of intermediate value theorem: if is a continuous function whose domain…

Q: Show that the given function is not analytic at any point but is differentiable along the indicated…

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Q: (6) If f(z) is analytic function show that: [v] + [0] =

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