I need a clear explanation about the radius function of the volume shell. In part a, the radius function is 2 - x, and in part b, the radius function is x + 1. Could I have an explanation as to why that is?

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A: Solution-Now differentiate this function with respect of x,d/dx(f(x))=f'(x)

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A: Since you have asked multiple questions, we will solve the first question for you.If you want any…

Q: (b) sin(y²) dyda 0 X

A: The given integral is

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A: f'(x)=x(x-4)

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A: Given that E and F are mutulayy exclusive

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A: Let . To find the equation of the tangent line to the graph of  at the point .

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A: The given integral is 5+secxtanx-sec2x

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A: To find the following integral.

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Q: Find the value or values of c that satisfy the equation 4 f(x)= 4x+- f(b)-f(a) b-a =(Use a comma to…

A: The given function is .The aim is to find the value of .

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Q: 25. f(x) = 2x³/5 - x6/5; c= 0.

A:

Q: If f(x) = 6 + 3x − 2x², find f'(4).

A: Given,

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A: Increasing function : f'(x) &gt;0Decreasing function: f'(x)&lt;0

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Q: : Evaluate 99 Σcos (km) k=1

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A: Given equation 2tan2x +sec2x -2=0 Using identity sec2x =1+tan2x, we get2tan2x + 1+tan2x -2=0

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A: To find all -intercepts of the following function.

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A:

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A: As per guidelines, we can solve only first 3 subparts if multiple subparts are posted. Please repost…

Q: Find the torsion of the space curve. r(t)=(2t-7)i+(t²-2)j+7k

A: r(t)=(2t-7)i+(t²-2)j+7k

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Q: Maximize p = 2x + 3y + 5z 2y + 2y + Y + Subject To: 2x + X ++ X + IA IA IA 2 3x < z 10 15 40

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Q: +'? 14 w on e H on At the point shown on the function above, which of the following is true? O f' 0…

A: According to the given graph

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Q: Find the standard equation of the circle with center(2,-5) and radius 2.

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Q: ·S 61. cos (1/x) x2 dx.

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Q: sinx x0 e²x-1 5. Use power series to evaluate lim

A: Power series expansion

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Q: Given: (x is number of items) 4800 Demand function: d(x) = Supply function: s(x) = 3√x Find the…

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Q: Suppose that f(x, y) = 2x² + 2y¹ − 2xy Then the minimum is

A: Given function: f(x,y)= 2x4+2y4-2xy partially differentiating f w.r.t. x, ∂f∂x= 8x3-2y partially…

Q: Verify that (sin(0) csc(0))+ (cot(0) tan(0)) = 2

A: We have to verify,

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Q: Evaluate the indefinite Integral, (Use C for the constant of integration.) [ 0² (3+70² 7693/2 dr

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A: Solution is following in explanation step.

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A:

Q: Use the Euclidean algorithm to find 4. a) god(200, 277) b) gcd(1001, 1331)

A: 4) a) gcd(200,277)b) gcd(1001,1331)

Q: Find and classify the critical points of (x² - 6x) (y² – 7y) 2= Local maximums: Local minimums:…

A: z=(x2-7y)

Q: -3 If A = [¯ 1¹ ²], B = [~ 3³ 2], and C = =[2], find 4 21 A²+ BC.

A:

Q: Let f(x) = x sin^2x, g(x) = x cos^2x, and h(x) = x. Then the functions f, g, and h are linearly…

A: