ISC (Commerce) Class 12CISCE
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Using L'Hospital'S Rule, Evaluate : `Lim_(X->0) (X - Sinx)/(X^2 Sinx)` - ISC (Commerce) Class 12 - Mathematics

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Question

Using L'Hospital's rule, evaluate : `lim_(x->0) (x - sinx)/(x^2 sinx)`

Solution

`lim_(x->0) (x-sinx)/(x^2 sinx)`

`= lim_(x-> 0)  (1-cos x)/(x^2 cos x + sin x. 2x)`

`= lim_(x->0)  (2sin^2 x/2)/(x^2(cos x + (2sinx)/x)) = (2sin^2 x/2)/(4xxx^2/4(cos x + (2sinx)/x))`'

`= lim_(x- > ) 2/(4(cosx + 2))`

`= lim_(x -> 0)  1/(2(3))  = 1/6`

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APPEARS IN

 2014-2015 (March) (with solutions)
Question 1.4 | 3.00 marks
Solution Using L'Hospital'S Rule, Evaluate : `Lim_(X->0) (X - Sinx)/(X^2 Sinx)` Concept: L' Hospital'S Theorem.
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