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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: Limits involving inverse
Forum Index -> Differential Calculus like the article? email it to a friend.  
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nasa_hs (25)

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Olaaa!! Perrrfect answer. 5  [5 rates]

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limxa  sin-1x -sin-1a / x - a
limx/6  sin(x-/6) / 3  - 2cosx  (root sign is only for 3)
 
    
elessar_iitkgp (2220)

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Olaaa!! Perrrfect answer. 380  [540 rates]

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You can solve both by LH rule ... but lets try a different tune.
First problem
xa (sin-1x - sin-1a) / (x - a)
= ( - )/(sin - sin ) where sin-1x = and sin-1a =
= ( - )/2cos[( +)/2]sin[( -)/2]
=(( - )/2)/sin[( -)/2] x (2/cos[( +)/2])
=1 x 2
=2

Second problem
x/6 sin (x - /6) / 3 - 2cos x
=x/6 sin (x - /6) / 2( 3/2 - cos x)
=x/6 sin (x - /6) / 2(cos/6  - cos x)
= x/6 2sin [(x - /6)/2] cos[(x - /6)/2]/ 4sin [(x + /6)/2]sin [(x - /6)/2]
=x/6 (1/2)[cos[(x - /6)/2]/sin [(x + /6)/2]]
=(1/2) x 1 / (1/2)
= 1



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