d'y (3x* – 5)(2.x² +9x–6) Determine the of y = 3 dx 7x

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A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

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A: The given function,   f(x)=x-12+x+12

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A: We solve the given initial value problems below.

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A: Question number 1 has been solved as per the prescribed format.

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A: Firstly separate the variables and integrate on both sides and solve the differential equation.…

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A: Solved below.

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A: Solving

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A: Integral test

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A: Solution

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A: To find the sum of the given finite series. Note that: ∑i=1n1=n∑i=1ni=n(n+1)2∑i=1ni2=n(n+1)(2n+1)6

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A: topic- indefinite integral

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A: Inverse Laplace transform shifting property:

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A: We can find the dot product as below.

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A: The given function is: f(x)=x5+4x3+x, a=4f(4)=45+4(43)+4=1284f'(x)=5x4+12x2+1,…

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A: We can solve this as follows:

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A: To find out dw/dt.

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A: answer is in next step

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A: answer is in next step

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A: Topic = Functions Correct option  = c

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A: Plane travels for 9.5 hours on two-way trip between location A and B. The Plane can fly at 320 km/h…