IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

elastiboysai

Re:Limit

elastiboysai

Re:Limit

hsbhatt

$lim_{x ightarrow pi} rac{1}{x-pi}(sqrt{ rac{4cos^2x}{2+cosx}}-2)$

L'Hospital's rule is quite alright. But the fastest way to getting at this one is:

let f(x) =

4cos²x/2+cosx. Then f(

) = 2

So, the problem is lim (f(x) - f(

))/(x-

) which is nothing but f'(x) at x=

.

x

You get the answer in no time as zero.

(x-

) in the denominator when x

gives the 1st clue that some mischief like this is intended.