calculus problem on limits

Question

Comments

Answer: 1 ?

Answer 1

It is 0^0 formate apply L hospital

= e ^ limt x-> 0 (sinx ln x)

e^ limt x->0 (lnx/cosecx) apply L hospital

e ^ limt x->0 (-(sinx/x cotx))

e ^ 0

=1

Answer 2

1 fx power gx type function

Answer 3

DIRectly substitute value of x

Answer is 1

Answer 4

This problem is in 0^0 form so, we cant apply L Hopital Rule .

Please follow the below step and you will get the answer.

Take Log on both the side and bring the limit in O/O form .

Apply L Hopital and solve further.