The signum (or sign) function, denoted by sgn, is defined by (a) Sketch the graph of this

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The signum (or sign) function, denoted by sgn, is defined by


-1 if x<0 O if x=0 I if x>0 sgn x

(a) Sketch the graph of this function.
(b) Find each of the following limits or explain why it does not exist.
(i) limx→0+ sgn x
(ii) limx→0- sgn x
(iii) limx→0 sgn x
(iv) limx→0 | sgn x |
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