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(i)lim(x->0) ((sqrt(1+x)-sqrt(1-x))/x)(i...

(i)`lim_(x->0) ((sqrt(1+x)-sqrt(1-x))/x)`(ii) `lim_(x->0)(x-sinx)/x^3`

Text Solution

Verified by Experts

`=lim_(x->0)(1-1+2sin^2(x/2))/(sin^2x)`
`=lim_(x->0)((sin(x/2))/(x/2))^2*((x/2)^2/(sinx/x))x^2`
`=lim_(x->0)(2*x^2/4*1/x^2)=1/2`.
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