self doubt

Question

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

can we straight away say $0^{0}=0$  ?

Comments

Cos0 =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

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Thanks, Corrected the question.

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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 !

Answer 1

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

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