17_Cal_Solution of Calculus_6e

17_Cal_Solution of Calculus_6e - f[x ] := Floor[ 2 ∗ x ];...

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Unformatted text preview: f[x ] := Floor[ 2 ∗ x ]; Plot[ f[x], { x, − 3 . 5, 3 . 5 } , AspectRatio − > Automatic, PlotRange − > {{ − 3 . 5, 3 . 5 } , {− 4 . 5, 4 . 5 }} ]; Mathematica will draw vertical lines connecting points that it shouldn’t, making the graph look like treads and risers of a staircase, whereas only the treads are on the graph. C01S02.054: The function f is undefined at x = 1. The graph consists of the horizontal line y = 1 for x > 1 together with the horizontal line y = − 1 for x < 1. There is a discontinuity at x = 1. C01S02.055: Given: f ( x ) = [[ x ]]. If n is an integer and n 5 x < n + 1, then express x as x = n + (( x )) where (( x )) = x − [[ x ]] is the fractional part of x . Then f ( x ) = n − x = n − [ n +(( x ))] = − (( x )). So f ( x ) is the negative of the fractional part of x . So as x ranges from n up to (but not including) n + 1, f ( x ) begins at 0 and drops linearly down not quite to − 1. That is, on the interval ( n,n + 1), the graph of f is the straight...
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This note was uploaded on 09/14/2011 for the course MATH 101 taught by Professor Cheng during the Spring '11 term at Ecole Hôtelière de Lausanne.

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