0 votes 0 votes $\lim_{x\rightarrow \frac{\pi }{2}}cosx^{cosx}$ can we straight away say $0^{0}=0$ ? Calculus calculus + – manisha11 asked Jan 5, 2019 edited Jan 5, 2019 by srestha manisha11 356 views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply Peeyush Pandey commented Jan 5, 2019 reply Follow Share Cos0 =1 and yes 1^1=1 0 votes 0 votes arvin commented Jan 5, 2019 reply Follow Share 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 0 votes 0 votes manisha11 commented Jan 5, 2019 reply Follow Share Thanks, Corrected the question. 0 votes 0 votes arvin commented Jan 5, 2019 reply Follow Share 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... 2 votes 2 votes manisha11 commented Jan 5, 2019 reply Follow Share THANKSS 0 votes 0 votes Nandkishor3939 commented Jan 5, 2019 reply Follow Share Nice approach ! 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Yeah when x-->0 then cos(x) approches 1 i.e. value of cos(x)^cos(x) will be 1^1 = 1 Nandkishor3939 answered Jan 5, 2019 Nandkishor3939 comment Share Follow See all 0 reply Please log in or register to add a comment.