Unformatted text preview: that f ( a ) n = b for any a ∈ R . As an example, if b = 8, then we would need that a 2 =1 3 . 2) Find the least integer n such that f ( x ) is O ( x n ) for each of these functions. a) f ( x ) = 2 x 2 + x 3 log x 2 x 2 is O ( x 2 ), while x 3 log x is O ( x 3 log x ). But log x < x , so x 3 log x is O ( x 4 ). Thus, when we add these two functions, we get that f ( x ) is O (max( x 2 ,x 4 )) = 0( x 4 ). Thus, the answer is n = 4. b) f ( x ) = ( x 3 + 5 log x ) / ( x 4 + 1) We can say the top is O ( x 3 ), while the bottom is O ( 1 x 4 ). So when you multiply the two functions together, you get O ( 1 x ). 1...
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This note was uploaded on 08/11/2008 for the course MATH 240 taught by Professor Miller during the Fall '08 term at University of Wisconsin.
 Fall '08
 Miller
 Math

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