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JEE Class main Answered

Please solve without using L'hopital rule
Asked by g_archanasharma | 06 Mar, 2019, 06:09: AM
Expert Answer
begin mathsize 16px style limit as straight x rightwards arrow 0 of space fraction numerator 3 to the power of 2 plus straight x end exponent minus 9 over denominator straight x end fraction
equals limit as straight x rightwards arrow 0 of space fraction numerator 3 squared cross times 3 to the power of straight x minus 9 over denominator straight x end fraction
equals limit as straight x rightwards arrow 0 of space fraction numerator 9 cross times 3 to the power of straight x minus 9 over denominator straight x end fraction
equals limit as straight x rightwards arrow 0 of space fraction numerator 9 open parentheses 3 to the power of straight x minus 1 close parentheses over denominator straight x end fraction
equals 9 limit as straight x rightwards arrow 0 of space fraction numerator open parentheses 3 to the power of straight x minus 1 close parentheses over denominator straight x end fraction
equals 9 log 3
equals log 3 to the power of 9 end style
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