السؤال الثالث Question Three * Q3. For the motion vector r(t) = et cost i + et sint j , find: (i) N (ii) ат قمت بالإجابة على السؤال الثالث >

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A: Plane and line

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A: As per our guideline if multiple questions are posted we are supposed to answer only the first one.

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A: To evaluate the integral.

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A: Use change of order of integration.

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A: To find the maximum hight of the ball.

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A: Firstly we can find Limits and In second one we can find partial derivatives .

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A: Given, ∫ x27+6x-x2dx

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A: A detailed solution is given below.

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A: Given graph of a function f.

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Q: 1. n² Determine whether the series Σn=13n+1 ln(n+1) is convergent or divergent.

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A: This question is based on diffrential equation solved using Laplace transform.

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A: John invested his inheritance of $12,000 in three different funds: part in a money-market fund…

Q: 3. Consider the vectors X and Y in R³ where X = i +3j and Y = 4i - 2j+2k. Find the unit vector…

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Q: Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate…

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Q: 10 5(5+10) a/n A ナ B 5+10

A: See the details solution in below

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A: We have to calculate the rate of change after 1 hours

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: Identify ALL the Indeterminate forms involved and determine the limit of: limo+ (cos(x))"

A: See the answer below

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

A: : since,1< ln(n+1),for n>2 so, 0<(n^2)/(((3^(n+1))*ln(n+1))<n^2/n^4=1/n^2,  since…

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A: Given.

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Q: Evaluate S 2 dx √x4+25

A: ∫1au+b du = 1alnau+b+C

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