Which of the following represents the region of the complex plane defined by |z−2i-3| ≤2? (A) Imaginary 3 1 4 0 3 (C) Imaginary 2 0 O 2 1 5 Real Real (B) Imaginary 0 (D) Imaginary 4 O 1 4 5 Real Real

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A: To find the value of a and b.

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A: Given :∫∫Rsinx2+y2dAR :Radius of unit circle is 3 and 4

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A: Topic = Derivative

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A: Area enclosed by curve r=f(θ), α≤θ≤β is given by  Area = 12∫αβr2dθ

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A: Given :f(x)=gx4g'(81)=6

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A: Given

Q: 2) Find the radian measure of angle 0 in the figure below. 22.5. a) O 2.25 radians b) O 4.5 radians…

A: we know that arc 2πR =2π radians

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A: Here we have to write the equations in matrix form and then we have to do matrix multiplication.

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A: Solution is given below:

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Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

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Q: Problem 1. Solve these integrals using substitution (a) x(x-2)³ dx, (b) text² di dt.

A: The given integrals:a∫xx-25dxb∫te3t2dtWe will solve them using substitution.

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A: Topic = Limits Just 1 is true.

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A: We have to solve above question Two opposite number have a sum of 0

Q: 11. Integral sin³ R cos R dR

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A: option (A)  is correct. see below the calculation

Q: Please provide Handwritten answer of all parts.

A: Please provide Handwritten answer of all parts.

Q: Question 1. A critical point of the function g(x, y) = ex y + 3x²y-y is (0,0). Use the Second…

A: Explained below

Q: CHECKPOINT 1.13 Find the average value of f(x) = 6 - 2x over the interval [0, 3] .

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A: The given data is: limh→0f10+h-f10h=-5

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A: According to question,Given Function,fx = 3-5x3P0, 3Qx, fx

Q: 1 f(x) = X g(x) = Inx A) In[f(x) + c C) Inf'(x) + c 1 1+2e-x A) In|1+2e C) Inje*+1| + c 5. f(x) g(x)…

A: We can answer both the question as below.

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A: Given :I=∫01dz7z+16

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Q: limg-0 2x sinx 4-4cosx

A: We can find the limit as below, using L'Hospital rule.

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Q: 2 2. √(√x-3) dx

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…