# mid1v - P (0 , , 0), Q (1 , 2 , 3), R (2 , 3 , 4), S (3 , 5...

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Math 126 DA- Spring 2007 Midterm 1 April 19, 2007 Name: Student ID Number: 1 10 2 10 3 10 4 15 5 15 Total 60 You are allowed to use a scientiﬁc calculator only (no graphing calculators) and one, hand- written , double-sided page of notes. Check that your exam contains all the problems listed above. You must show your work on all problems. The correct answer with no supporting work may result in no credit. If you need more room, use the backs of the pages and indicate to the grader that you have done so. Leave answers in exact form. Remember to check your work.

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1. (10 points) Find the Taylor series for f ( x ) = 1 (1 - x )(1 - 3 x ) based at b = 0 and ﬁnd the interval of convergence.
2. (10 points) Consider the two vectors a = h 1 , 2 , 3 i and b = h 2 , 3 , 4 i . Calculate the following: (a) (4pts) The cosine of the angle between a and b (b) (4pts) a × b (c) (2pts) The area of the parallelogram with corner points

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Unformatted text preview: P (0 , , 0), Q (1 , 2 , 3), R (2 , 3 , 4), S (3 , 5 , 7) 3. (10 points) Consider the function f ( x ) = sin( x ) (a) (5pts) Find the second Taylor polynomial, T 2 ( x ), for f based at b = π/ 2. (b) (5pts) Find an interval J containing b = π/ 2 such that the error, | f ( x )-T 2 ( x ) | is less than . 01 for all x in J 4. (15 points) Consider the function f ( x ) = Z x e t-1 t dt (a) (10pts) Find the Taylor series for f ( x ) based at b = 0 (b) (5pts) Find f (6) (0) 5. (15 points) Let v = h 1 , 3 ,-1 i and r = h 1 , 1 , 1 i and consider the line given by, r = r + t v , in vector form. Also consider the plane given by x + 2 y + 2 z + 2 = 0 (a) (5pts) Show that the line and the plane are not parallel (b) (10pts) Find a point on the line at distance 3 from the plane...
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## This note was uploaded on 05/07/2008 for the course MATH 126 taught by Professor Smith during the Spring '07 term at University of Washington.

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mid1v - P (0 , , 0), Q (1 , 2 , 3), R (2 , 3 , 4), S (3 , 5...

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