how the mode value is open in LhL and rhL in continity when h tends to zero

Asked by onam singla | 10th Apr, 2011, 12:00: AM

Expert Answer:

When h →0, it means h is not equal to zero but it is very near to zero.
 
For LHL we take h→0¯, it means that h is nearer to zero from left side i.e. h is less than zero.
For RHL we take h→0+, it means that h is nearer to zero from right side i.e. h is greater than zero.
The function |x| is defined as
     |x| = x  if x ≥ 0
or,  |x| = —x  if x < 0
In case of LHL when h→0¯, take |x| = —x.
and in case of RHL when h→0+, take |x| = x.

Answered by  | 10th Apr, 2011, 09:55: AM

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