Math%20119%202005-2006%20Fall%20MidTerm2

Math%20119%202005-2006%20Fall%20MidTerm2 - METU Department...

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Unformatted text preview: METU Department of Mathematics CALCULUS I Mid Term 2 Last Name : : Name Department : : Signature 1 2 : December.10.2005 : 09:00 : 120 minutes 3 4 5 6 QUESTIONS ON 6 PAGES TOTAL 60 POINTS 6 SHOW YOUR WORK UĞU Date Time Duration Student No. : : Section Z : Math 119 Code Acad. Year : 2005-2006 : Fall Semester Coordinator : Muhiddin Uguz √ Question 1 (4+2+4=10 points) Let f (x) = 3 x(x − 1) be defined on [−1, 1]. iddin a)Find local extremas of f (x) Muh b)Find the absolute extremas of f (x) c)Approximate f (0, 98) by linearization Question 2 (4+4+4=12 points) Evaluate the limits. If you use a theorem or a well known limit, state it explicitly. n 1 k 15 a) lim n→∞ n n b) lim sin(t) t dt x 2x − 1 x→0 3x − 1 c) lim Muh iddin x→0 x2 x UĞU Z k=1 Question 3 (4+4+4=12 points) Find the following integrals x5 x3 + 1 dx tan3 (x) dx 0 c) x2 sin(x) dx iddin b) Muh π 4 UĞU Z a) Question 4 (3+2+2+3=10 points) Let f (x) = x2 x2 − 1 UĞU Z a)Find all asymptotes of the graph of f (x) iddin b)Find the intervals where f (x) is increasing and the intervals where f (x) is decreasing Muh c)Find the intervals where f (x) is concave up and the intervals where f (x) is concave down d)Sketch the graph of y = f (x) (Show the intercepts) Name, Surname:......................................... Student Id:...............Section:.......... Question 5 (8 points) A point is moving to the right along the first-quadrant porsion Muh iddin UĞU Z of the curve x2 y 3 = 72. When the point has coordinates (3, 2), its horizontal velocity is 2 units/s. What is its vertical velocity? Question 6 (4+4=8 points) Let f (x) = 2x + 1 8 if 0 ≤ x < 2 if 2 ≤ x < 5 5 a) Find f (x)dx. UĞU Z 0 5 b)Show that there is no c ∈ [0, 5] such that f (x)dx = f (c)(5 − 0). Why does this not 0 Muh iddin contradict the Mean Value Theorem for Integrals? Explain your answer. ...
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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%202005-2006%20Fall%20MidTerm2 - METU Department...

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