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Plz help me solve this question...

Answer»

Check: as x→π/4 
4√2 - (cos x + sin x)^5 becomes 0 
1 - sin(2x) becomes 0 

use L'Hopital's rule then . 


= lim [-5(cos x + sin x)^4 (-sin x + cos x)] / [-2 cos(2x)] 

= lim [5(cos x + sin x)^4 (-sin x + cos x)] / [2 {cos^2(x) - sin^2(x)}] 

= lim [5(cos x + sin x)^4] [2 (cos x + sin x)] 
= lim (5/2) (cos x + sin x)^3 
= (5/2) (2√2) 
= 5√2 .


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