JEE Class main Answered
Please solve without using L'hopital rule
![question image](https://images.topperlearning.com/topper/new-ate/topr_21545817745488402IMG20190306060203.jpeg)
Asked by g_archanasharma | 06 Mar, 2019, 06:05: AM
![begin mathsize 16px style limit as straight x rightwards arrow 0 of space fraction numerator square root of 1 plus 2 straight x end root minus square root of 1 minus 2 straight x end root over denominator sinx end fraction
equals limit as straight x rightwards arrow 0 of space fraction numerator square root of 1 plus 2 straight x end root minus square root of 1 minus 2 straight x end root over denominator sinx end fraction cross times fraction numerator square root of 1 plus 2 straight x end root plus square root of 1 minus 2 straight x end root over denominator square root of 1 plus 2 straight x end root plus square root of 1 minus 2 straight x end root end fraction
equals limit as straight x rightwards arrow 0 of space fraction numerator 1 plus 2 straight x minus 1 plus 2 straight x over denominator sinx end fraction cross times fraction numerator 1 over denominator square root of 1 plus 2 straight x end root plus square root of 1 minus 2 straight x end root end fraction
equals limit as straight x rightwards arrow 0 of space fraction numerator 4 straight x over denominator sinx end fraction cross times fraction numerator 1 over denominator square root of 1 plus 2 straight x end root plus square root of 1 minus 2 straight x end root end fraction
equals limit as straight x rightwards arrow 0 of space fraction numerator 4 over denominator begin display style sinx over straight x end style end fraction cross times fraction numerator 1 over denominator square root of 1 plus 2 straight x end root plus square root of 1 minus 2 straight x end root end fraction
equals 4 over 1 cross times fraction numerator 1 over denominator 1 plus 1 end fraction
equals 2 end style](https://images.topperlearning.com/topper/tinymce/cache/949b5205884c6b00bdf31df38fa65a97.png)
Answered by Sneha shidid | 06 Mar, 2019, 09:34: AM
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