find limit as x approaches pi/2
of x sec^2 x

Question

find limit as x approaches pi/2
of x sec^2 x

ikram002p · Answer

as you know sec ^2 pi/2
does no exist  ,

ikram002p · Answer

so we need to find a trick for how doing it
sec x=1/cos x right ?

anonymous · Answer

yes
and cos pi/2 is 0

ikram002p · Answer

then 

lim x sec^2 x = lim x / cos ^2 x

do you know LH rule ?

anonymous · Answer

dont think so

ikram002p · Answer

LH means   for g(x)/h(x)
limit g(x) / f(x) = limit g'(x) / f'(x)

ikram002p · Answer

so for what you have 
 lim x / cos ^2 x = limit x' / (cos^2 x) ' = limit 1/ -2 sin x

ikram002p · Answer

hence :-
limit  1/-2 sin x as n goes to pi/2 = -1/2 :)
does that make sense to u ?

anonymous · Answer

i think so yes

ikram002p · Answer

:D 
cool then done thats it :P

anonymous · Answer

tyvm for the help

ikram002p · Answer

anonymous · Answer

i will take a look now

dumbcow · Answer

@ikram002p, LH rule does not apply here, the limit is not indeterminate .... 0/0 or inf/inf also the derivative for cos^2 is wrong, it should be ---> 1/-2sincos limit of C/0 = infinity http://www.wolframalpha.com/input/?i=lim+x*sec%5E2+x+as+x-%3Epi%2F2

anonymous · Answer

it can also be solved by converting term containing "cos"into sin and applying "sinx/x" or "x/sinx" =1.