Reference no: EM13979323
1. What do you understand from Curl and Div of a vector field F? Explain them with examples. Is there any difference between Grad and Div of F? What are the applications of Grad, Div and Curl?
2. Find the area of a parallelogram spanned by the vectors 
and 
3. State and Prove Cayley-Hamilton theorem. Using Caley-Hamilton theorem find the inverse of the matrix
A = 
4. Define Contra positive, Converse, and Inverse of a statement. What are the contra positive, the converse, and the inverse of the conditional statement "The home team wins whenever it is raining?". Give an example of statement is a Tautology. Justify your example.
5. Prove without contradiction, that if n is an integer and n2 is odd, then n is odd. Can this be proved using contradiction? If so, prove using contradiction also.
6. Verify that the conditions of Rolle's Theorem are satisfied by the function f(x)= 3x4-2x3-2x2+2x, x ∈[-1,1], and determine a value of c in (-1,1) for which f' (c)= 0. Is Rolles' theorem related Mean value theorem? If yes, how is it related? What is the significance of Mean Value theorem?
7. What do you understand by series being conditionally convergent and absolutely convergent? Determine whether the series 
are absolutely convergent, conditionally convergent or divergent.
8. Determine the radius of convergence of each of the following power series: 
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What is the combined effect of curvature
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Sharing confidential information
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Normal level of activity for the project
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Find the magnitude and direction of the total magnetic field
: At some instant, an alpha particle(q=+2e) has the coordinates(3.0,0.0,0.0)(nm) and is moving along the positive x-axis with 500km/s while an electron at (0.0,4.0,0.0)(nm) is moving along the negative y-axis with 1000km/s. Find the magnitude and di..
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What do you understand from curl and div of a vector field f
: What do you understand from Curl and Div of a vector field F? Explain them with examples. Is there any difference between Grad and Div of F? What are the applications of Grad, Div and Curl? Define Contra positive, Converse, and Inverse of a statement..
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What was the cars velocity when it passed the checkpoint
: A speeding car passes a highway patrol checkpoint and thendecelerates at a constant rate. What was the car's velocity when it passed the checkpoint? What was the acceleration of the car?
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What is supply and demand how do they differ
: What is Supply and Demand? How do they differ?
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Draw correct and complete free-body diagrams
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Bad-news messages critique paper
: This is the fourth of five weekly Business Communication Analysis papers you will complete in this course. This exercise is designed to deepen your understanding of the business communication process.
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