Cos0 =1

and yes 1^1=1

and yes 1^1=1

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no we cant straight away say that 0^0 = 0 , its an indeterminate form..

but when you put x->0 in the given f(x) it gives 1^1 = 1 which is acceptable..

refer this : http://tutorial.math.lamar.edu/Classes/CalcI/LHospitalsRule.aspx