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Asked by sarveshvibrantacademy | 15 May, 2019, 11:25: AM
answered-by-expert Expert Answer
begin mathsize 16px style limit as straight x rightwards arrow 2 of space open parentheses straight x minus 1 close parentheses to the power of fraction numerator 1 over denominator 2 minus straight x end fraction end exponent
Put space straight x equals 2 plus straight h
hence comma space straight h rightwards arrow 0
limit as straight h rightwards arrow 0 of space open parentheses 2 plus straight h minus 1 close parentheses to the power of fraction numerator 1 over denominator 2 minus 2 minus straight h end fraction end exponent
limit as straight h rightwards arrow 0 of space open parentheses 1 plus straight h close parentheses to the power of fraction numerator 1 over denominator negative straight h end fraction end exponent
limit as straight h rightwards arrow 0 of space open square brackets open parentheses 1 plus straight h close parentheses to the power of 1 over straight h end exponent close square brackets to the power of negative 1 end exponent
straight e to the power of negative 1 end exponent end style
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