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Please solve without using L'hopital rule

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Asked by g_archanasharma | 06 Mar, 2019, 06:05: AM

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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

Answered by Sneha shidid | 06 Mar, 2019, 09:34: AM

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