The Gateway to Computer Science Excellence
0 votes
54 views
$\lim_{x\rightarrow \frac{\pi }{2}}cosx^{cosx}$

can we straight away say $0^{0}=0$  ?
in Calculus by Active (2.3k points)
edited by | 54 views
0
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

0
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...
0
THANKSS
0
Nice approach !

1 Answer

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

i.e. value of cos(x)^cos(x)  will be 1^1 = 1
by Active (1.3k points)
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,737 questions
57,306 answers
198,321 comments
105,014 users