2r cos 0 Replace the polar equation r= (csc 0)3e2rc with an equivalent Cartesian equation. T

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A: M=d dx(g(f(x))

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A: The solution is shown below-

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A: The given curve is: y=1+x2-1

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A: Here we have to use the concept of integration

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A: The objective is to express the number as a ratio of integers .

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A: Given function:- fx=9πx2cosπx

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A:

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A: Since you have posted multiple questions i can do first question as per our company guidelines…

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A: Given that q(x)=−4x^4+5x^3+7x^2-10x+2 Since all coefficients are integers, we can apply the rational…

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A: We have  fx=6x+sin6xx∈0,2π

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A: The rate of intake, R, during a respiratory cycle for a person at rest is proportional to a sine…

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A: Given that curve for a drug is given by R=1001+100e-0.1x

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A: We are authorized to answer three subparts, so we answering the first three subparts.

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A: (1) f(x)=10x3-15x2-60x-30d dx(xn)=nxn-1d dx(constant)=0

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A: Velocity vectors÷ For wind  w→=50(sin30 i +cos30 j ) For jet  v→ =775(-sin30 i + cos30 j )

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A: Given: Find the general solution to the system x'= Ax, where  A=1-51-3

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A: Box

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Q: 37. lim x40+ log₂ x log, 3x

A: Note: Since, the student has mentioned to solve question no. 37,  so we solving according to this…

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A:

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A: We have given the rate of annual flow,f(t)=900 t e-0.1t

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A: We have to find the area according to the given information

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Q: x 16. Evaluate sin dx. f x +C O O- 1 3 cos³x 1 3 cos³x 1 2 cos²x 1 O- + C +C + C 2 cos²x ONone of…

A: we have to slove above integrate

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A: A detailed solution is given below.

Q: Expand f(x) = 4x² + 10x + 10 as a power series around x = -1. f(x) = (x + 1)² + (x + 1) +

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Q: an- If the nth partial sum of a series an is sn = 7 - n5-, find an and Σ n = 1 n = 1 n = 1 a1 an = =…

A: If the nth partial sum of a series ∑n=1∞ an is sn=7-n·5-n, then to find a1, an and ∑n=1∞ an.