For first pat
limx→0xSin−12x
Apply L.hospital rule in above equation,
limx→01−4x22
Now putting the limit
we get
= 1−02
=2
Now second part the given limit is
limx→0xcosecx−1
limx→0xcosecx1
This limit does not hold good for L.hospital rule, So the given limit diverges to ∞
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