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by: 2409385072

Math Math 215


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Calculus III
Divakar Viswanath
Class Notes
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This 2 page Class Notes was uploaded by 2409385072 on Monday September 19, 2016. The Class Notes belongs to Math 215 at University of Michigan taught by Divakar Viswanath in Fall 2016. Since its upload, it has received 4 views. For similar materials see Calculus III in Math at University of Michigan.


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Date Created: 09/19/16
Math 241 Matlab Project 1 For this project you will need to turn in a printout of your published m-▯le. See the guide for instructions on how to write and publish an m-▯le. Unless speci▯ed, all of the work should completely and clearly be done on Matlab. There are a total of 35 points for this project. Your TA might allow you to submit the project online. Ask your TA about it. If you submit it online it has to be done before your discussion starts on the due date. Part I due Tuesday, September 13, 2016 at the beginning of your discussion 1. (1 pt) Clear Matlab with clear all. 2. (1 pt) De▯ne the symbolic variables x and t. 3. (1 pt) Set t to be a real variable. 4. (1 pt) Factor the polynomial 3x + 28x + 88x + 90x ▯ 27x ▯ 54. 2 2x▯1 5. (1 pt) Di▯erentiate the function f(x) =tan xx ) + Part II due Thursday, September 29, 2016 at the beginning of your discussion 6. (1 pt) Evaluate the derivative of the function g(x) at x = 0.e 7. (1 pt) Integrate e cosx. 8. (1 pt) Find the area under the graph of f(x) = 4 ▯ x and above the x▯axis. ▯ ▯ 9. (a) (1 pt) De▯ne the vectors u = (3;▯1;2) and v = (4;2;▯1). ▯ ▯ b) (2 pts) Find the projection of u onto v . ▯ ▯ c) (2 pts) Find the angle between u and v . ▯ ▯ d) (1 pts) Find a vector perpendicular to both u and v . 10. (3 pts) De▯ne four points A = (1;1;2);B = (▯1;0;2);C = (2;0;1) and D = (▯2;▯2;1). Using two subtractions and one cross product all on one Matlab line show that the lines through A and B is parallel to the line through C and D. 11. (3 pts) De▯ne the points P = (1;2;▯1) and Q = (3;2;1) and the vector n = (1;1;3). Using a subtraction and a dot product all in one line on Matlab show that Q is not on the plane through P and perpendicular ▯ to n . 12. (3 pts) De▯ne the points A = (2;0;3);B = (1;1;1);C = (0;1;▯1) and D = (1;▯1;2). Using ▯ve subtractions, two cross products and one dot product all on one Matlab line ▯nd the distance from point D to the plane through A, B and C. 13. (a) (1 pt) De▯ne the vector-valued function r (t) = sint i + cost j + (t ▯ 1) k. ▯ b) (1 pt) Find the unit tangent vector T (t). ▯ c) (1 pt) Find the acceleration r (t). 14. Plot each of the following: a) (1 pt) f(x) = (x ▯ 1) (x + 2) b) (2 pts) The vector valued function r (t) = (sint;cost;t). c) (2 pts) The line segment joining (1;2;▯3) and (1;0;2). d) (2 pts) The plane x ▯ 2y + 3z = 2. 15. (2 pt) Find the length of the curve r (t) = cost i + 2t j ▯ sint k from t = 0 to t = ▯.


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