Consider the initial-value problem y' + exy = f(x), y(0) = 1. Express the solution of the IVP for x>0 as a nonelementary integral when f(x) = 1. y= - U dt + What is the solution when f(x) = 0? y = What is the solution when f(x)=e*?

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A: To find the relative maximum and minimum of the function

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A: In this question, we need to find the second partial derivative of the given function.

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A: This question is based on continuity of function.

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A: Solution: 2x+y=0, x≥0 y = -2x

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A: Integrating the given function gives the antiderivative.

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A: f(x)=Bx2+6sqrt(x).

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A: Given: f(x)=ln3-2x,a=1

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A: See the answer below

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A: See the details solution in below

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A: The given dimenssions of ellipsoid area=25 mb=20mc=40 mthickness t = 1 m

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A: Here we have to find whether the given graph is continuous or not.

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A: Let's find limit of given function.

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A: A detailed solution is given below.

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A: Explained below

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A: This question can be solved using the concept of limit and continuity.

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A: The objective is to solve the above question.

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A: A detailed solution is given below.

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A: As per our guidelines, I can answer maximum three sub parts of a question. Since there are multiple…

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A: f denotes piece wise function .  Identify the interval where function is concave down

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Q: 5. Identify and sketch the graph of y = x² + 1 in R³. M

A: y=x^2+1 x=0 y=1 x -3 -2 -1 0 1 2 y 10 5 2 0 2 5

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A: First we will frame a question and then solve it.

Q: 1. Determine whether the series n=1 3n+1 ln(n+1) is convergent or divergent.

A: : since,1&lt; ln(n+1),for n&gt;2 so, 0&lt;(n^2)/(((3^(n+1))*ln(n+1))&lt;n^2/n^4=1/n^2,  since…

Q: Question 5 What is the limx→ [(ln(2x - 4)) - (ln(x+3))]? If your answer is a Whole Number Fraction…

A: limx-infinity [ln(2x-4)-ln(x+3)].

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Q: What is S (x² + 2x)² dx? + x³ + ³x² + C 4 S (x² + 2x)²dx = ¹x¹ + x³ + 4 f (x² + 2x)²dx = (x² + 2x)¹…

A: We know, ∫xndx= xn+1/(n+1)