3. Find a power series representation for the function. (Give your power series representation centered at r = 0.) En=1 In (6 - x)

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

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A: Follow next step

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A: The definite integral,      ∫01e18ti+e-tj+t kdt

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A: To solve the given boundary value problem.

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A: If the ratio of the successive terms of the sequence is constant then it forms a geometric sequence.

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A: We have to find given integral.

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A: According to bartleby guidelines I can only answer the first three subquestions. Please repost the…

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A: Solution in step 2

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A: We have to find integration.

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A: Let's find.

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A: We have to find the derivative of the above equation.

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Q: 3. Supply the missing integrand and limits of integration. 61y drdy fip (b) 62y dydz =- dr

A: Solve it.

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A: Given problem:-

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A: We can solve the differentia; equation as follows:

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A: The graph is shown below:

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A: Note: for given integral none of the option is correct match.I have solved as per integration by…

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A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Consider the differential equation y" – 11y" + 28y = 0 Write the auxiliary equation of the given…

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A: Given,            The circle whose diameter has endpoints of -2,4 and 8,-6.To find : Write the…

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A: Let's find.

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Q: x3 +4x2+37x+58 6. S: x(x2+4x+29)

A: To evaluate the given integral.∫x3+4x2+37x+58xx2+4x+29 dx

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A: Given differential equations y''-24y'-16y=0

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Q: Q3/ Find the area of zone bounded by curves: y= x² , y= 3x+8

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Q: . Determine the Total Area bounded by f(x) = x´ – 1 on the interval [- 2,2].

A: