Find the smallest value of k, k e N, for which the average value of S(x) = 12 x + k %3D on the interval [0, 1] exceeds 100. k =

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A: Differentiate with respect to x. 

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A: Here we have to solve the given initial-value problem.    2y'y"=1 , y(0)=2 , y'(0)=1 

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A: I am attaching image so that you understand each and every step.

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A: Solution is written in below steps.

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A: F=72- 2vma = 72- 2v14359.81 dvdt=72-2v∫(146.3) dv72-2v=∫ dtt=-146.32ln(72-2v)+Cv=0 at t=0C=146.32ln(...

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A: Use simple integration formula.

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A: NOTE: Refresh your page if you can't see any equations. . here the given interval is 

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A: Follow the odd, even function rule.

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A: Solution is written in below steps

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A: As per company guidelines we can solve first question. I hope that the given solution will help you....

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A: Let's find. 

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A: Question - (a) Given: fx,y=xy Formula used: ddxxn=nxn-1  

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Q: S sin 3xcos"3xdd

A: Given: ∫sin43xcos43xdx Let I=∫sin43xcos43xdx  ⇒I=116∫2sin3xcos3x4dx ⇒I=116∫sin46xdx

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A: Explained below 

Q: (x+ 2y - 1) dx + (2x +y+ ) dy - o LINE 1 let メ= u-1, dx = du ya v+, dy edy LINE 2 (u-1+2y + 1-1) du ...

A: Error 1 :-  Line 3   (u-1+2v+1-1)du+(2u-2+v+1+1)dv=0  CORRET LINE :- (u-1+2v+2-1)du+(2u-2+v+1+1)dv=0...