Math%20119%202004-2005%20Fall%20MidTerm2

# Math%20119%202004-2005%20Fall%20MidTerm2 - METU Department...

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Group List No. Last Name Name Student No. Department Section Signature : : : : : : : : : : : : : Code Acad. Year Semester Instructor Date Time Duration M E T U Department of Mathematics Calculus I Mid Term 2 Math 119 2004-2005 Fall November 27,2004 09:00 119 minutes 7 QUESTIONS ON 6 PAGES TOTAL 60 POINTS 1 2 3 4 5 6 7 Question 1 ( 8 points) a) Prove that x - x 3 6 < sin ( x ) , for all x > 0 Muhiddin UGUZ

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Question 2 ( 10 points) The graph of y = f ( x ) is given in the ﬁgure. Also given that df dx (2) = - 4 , df dx ( - 4) = - 3 and lim x 1 - df dx ( x ) = 1 a) Find the domain and the roots(i.e. zeros)of df dx ( x ) . (Explain!) b) Find the intervals on which df dx ( x ) is positive and the intervals on which df dx ( x ) is negative.(Explain!) c) Find the intervals on which df dx ( x ) is increasing and the intervals on which df dx ( x ) is decreasing.(Explain!) d) Find the horizontal and vertical asymptotes of df dx ( x )(Explain!) e) Sketch the graph of y = f 0 ( x ) = df dx ( x ) Muhiddin UGUZ
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## This note was uploaded on 11/01/2011 for the course CHEMICAL E CHEM-107 taught by Professor Bilinmiyor during the Spring '11 term at Middle East Technical University.

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Math%20119%202004-2005%20Fall%20MidTerm2 - METU Department...

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