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BOUNDED/UNBOUNDED FUNCTIONS AND AREAS UNDER BOUNDED FUNCTIONS
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Consider 
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Clearly
never shoots to infinity for any t. Hence,
is a bounded function.
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Other examples of bounded functions:
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- Unit step u(t)
 
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Fig.1. Unit step function
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Unbounded function:
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Observe 
as t increases, for example at t = 10 sec,
and at t = 20 sec 
. Clearly 
increases unboundedly as t increases. h(t) is an unbounded function or signal.
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As another example, consider
,at t = 1,
, hence 
is unbounded.
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If a function is bounded, the area under it may or may not be finite.
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Consider
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= 0+
 |
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On the other hand, consider
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Formal integration gives
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It is indeterminate, however we know that
 .
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Hence, 
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or
even though the exact value is indeterminate.
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COMMUNICATIONS
