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$\lim_{x\rightarrow \frac{\pi }{2}}cosx^{cosx}$

can we straight away say $0^{0}=0$  ?
in Calculus
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97 views
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Cos0 =1

and yes 1^1=1
0

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

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Thanks, Corrected the question.
2
for such questions take log both sides and than proceed by breaking rhs into more simpler parts which will be log(cosx)/(1/cosx) again in indeterminate form so differentiate both numerator and denominator and than put the value of lim x->pie/2 .

it will get reduced log y=0

 y= e^0 = 1 answer...
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THANKSS
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Nice approach !

1 Answer

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Yeah when x-->0 then cos(x) approches 1

i.e. value of cos(x)^cos(x)  will be 1^1 = 1

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