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# F07 Final Exam Answers Ma2253

Course Number: MATH 2253, Fall 2007

College/University: SPSU

Word Count: 1846

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Fall 2007 Math2253 Fianl Exam Review Dr. Taixi Xu Department of Mathematics, SPSU Math2253 - Review Problems for Final Exam Chpater 2: Limits and Continuity 1. If f ( x) x 2 2 x 2 , find (a) f (3) (5) (b) f (3 h) ( h 2 4h 5 ) f (3 h) f (3) (c) (h 4) h 2. Find the average rate of change of the function over the given interval or intervals. f ( x) x 3 1 ; a) [2, 3] (19) b) [2, 2 h] ( 12 6h h 2 ) 3. Find the...

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Johns Hopkins - MATH - 201
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Colby - MATH - 253
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Colby - MATH - 253
ma253, Spring 2007 - Problem Set 1 Solutions1. Problems from the textbook: a. Section 1.1, problems 5, 7, 9, *20, *28. Problems 5, 7, and 9 should be straightforward; the answers are in the back of the book. Let's do the other two. 20. The total de
Colby - MATH - 253
ma253, Fall 2007 - Problem Set 2 Solutions1. Problems from the textbook: a. Section 1.1, problem *46 The equations are x1 + x2 + x3 = 1000 .2x1 + .5x2 + 2x3 = 1000. Row-reducing and solving leads to 5a - 5000 x1 3 x2 = -6a + 800 , 3 x3 a where
Colby - MATH - 253
ma253, Fall 2007 - Problem Set 3 Solutions1. Problems from the textbook: a. Section 2.1 0 0 0 doesn't go to 0. 1. Not linear. For example, 0 0 y1 x1 3. Not linear. If we scale x2 by , the output becomes 2y2, which x3 y3 is not times the ori
Colby - MATH - 253
ma253, Fall 2007 - Problem Set 4 Solutions1. Problems from the textbook: a. Section 2.3 1 The inverse is 8 -3 . -5 2*2 The matrix is not invertible. *4 The inverse is3 2 1 2 -3 2 -1 1 2 0 - 1 . 2 1 1 2*12 Hard to do by hand; doing it with t
Colby - MATH - 253
ma253, Fall 2007 - Problem Set 5 Solutions1. Problems from the textbook: a. Section 3.1, problems *18, *22, *38, *48.*18. Row-reducing A gives rref(A) = 1 4 0 0so the image is spanned by the first row, which is the only one that has a pivot. So
Colby - MATH - 253
ma253, Fall 2007 - Problem Set 6 Solutions*1. Let P be the linear space of all polynomials (of any degree). Show that no finite set of polynomials {p1(t), p2(t), . . . , pm(t)} can span all of P. (Hint: since there are a finite number of polynomials