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10c_final

10c_final - Name Discussion Section No PID Time TAs name...

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Name: PID: Discussion Section - No: Time: TA’s name: Math 10C - Final (Lecture A, Winter 2007) Duration: 3 hours Please close your books, turn your calculators off and put them away. You can use one page of notes. To get full credit you should support your answers. 1. a) (3 points) Find the Taylor polynomial of degree 3 for e x about x = 0. Use this Taylor polynomial to approximate the Euler constant e . b) (3 points) Find the sum of the convergent series 1 + 1 1! + 1 2! + 1 3! + 1 4! + . . . # Score 1 2 3 4 5 6 7 8 Total

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2. Describe in words the graphs of the equations in 3-space in all parts. a) (2 points) x = y b) (2 points) x = y = z c) (2 points) z = 1 - x 2 - y 2
3. Let p = (0 , 1 , 0), q = ( - 1 , 1 , 2), r = (2 , 1 , - 1) be points in 3-space, -→ pq , -→ pr be the displacement vectors from p to q and from p to r , respectively, n be a normal vector to the plane containing p , q and r . You don’t need to calculate n to solve any of the parts. a) (2 points) Using the definition of a normal vector simplify -→ pq.n b) (2 points) Explain how you can obtain the normal vector n

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