A road with holes

Calculus Level 4

lim x 1729 f ( x ) f ( 1729 ) \large \displaystyle\lim_{x\to1729} {f(x) - f(1729) }

Let f ( x ) = x + x f(x) = \lfloor x \rfloor + \lfloor -x \rfloor , where \lfloor \cdot \rfloor denotes the floor function . Compute the limit above.

0 1729 -1 Limit does not exist 1

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1 solution

Rushikesh Jogdand
May 18, 2016

f ( x ) = { 1 x { R } { Z } 0 x { Z } f(x)=\left\{\begin{matrix} -1 & x \in \{\mathbb{R}\}-\{\mathbb{Z}\}\\ 0 & x \in \{\mathbb{Z}\} \end{matrix}\right.

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