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M17 LE3 Sem2 09-10

# M17 LE3 Sem2 09-10 - f x = x x-5-1 5 pts 2 Given f x = 4 x...

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MATH 17 LE3 | 02.12.10 SHOW ALL NECESSARY SOLUTIONS. WORK NEATLY. I. Fill in the blanks. Show your computations. 2 pts each 1. If f = {(2,3), (3,1), (0,2)}, then ( f - 1 f - 1 )(1) = ____________. 2. If k = log 9, then log 9 100 in terms of k is ____________. 3. The sequence e - 3 , 1, e 3 , e 6 is a ____________ progression with common ratio/difference ____________. 4. By Descartes’ Rule of Signs, the polynomial x 4 + x 3 - 2 x + 1 has ____________ positive real root/s and ____________ negative real root/s. 5. Suppose L is directly proportional to the square of m and inversely proportional to n . If both m and n are doubled, then L would be ____________. 6. The domain of the function f ( x ) = ln ( x - 3) is ____________. II. Find the solution set of the following. 5 pts each 1. 6 e 1 - x = 36 x (Express your answer in terms of r = ln 6.) 2. 2log 3 (1 - x ) = 1 + log 3 ( x + 5) 3. (log x 9) ± log 3 3 x 2 = 1 III. Do as indicated. 1. Find the inverse and the range of the function
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Unformatted text preview: f ( x ) = x x-5-1. 5 pts 2. Given f ( x ) = 4 x 4 + 4 x 3-x 2 + ax + 3, where a is an integer. (a) List all possible rational zeroes of f . 2 pts (b) Given that x + 1 is a factor of f , ﬁnd the value of a . 3 pts (c) Find all the zeroes of f . Indicate the multiplicity of each zero. 5 pts 3. Find the common ratio of an inﬁnite geometric progression whose sum is 4 and whose ﬁrst term is 4 5 . 3 pts 4. The ﬁrst and 13th terms of an arithmetic progression are-3 and 39 respectively. Find the sum of the ﬁrst 10 terms of the progression. 5 pts *END OF EXAM* Total: 50 points "It’s when things seem worst that you musn’t quit."-Anonymous /ajdporlante 01.22.10/ 1...
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