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Asked by sarveshvibrantacademy | 17 May, 2019, 09:31: AM
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begin mathsize 16px style limit as straight x rightwards arrow 1 of space fraction numerator straight e to the power of begin display style fraction numerator 1 over denominator straight x minus 1 end fraction end style end exponent minus 2 over denominator straight e to the power of fraction numerator 1 over denominator straight x minus 1 end fraction end exponent plus 2 end fraction Put space straight x equals 1 plus straight h straight x rightwards arrow 1 space rightwards double arrow straight h rightwards arrow 0 limit as straight h rightwards arrow 0 of space fraction numerator straight e to the power of begin display style 1 over straight h end style end exponent minus 2 over denominator straight e to the power of 1 over straight h end exponent plus 2 end fraction Put space 1 over straight h equals straight y straight h rightwards arrow 0 rightwards double arrow straight y rightwards arrow infinity limit as straight y rightwards arrow infinity of space fraction numerator straight e to the power of begin display style straight y end style end exponent minus 2 over denominator straight e to the power of straight y plus 2 end fraction equals limit as straight y rightwards arrow infinity of space fraction numerator straight e to the power of straight y open parentheses 1 minus begin display style 2 over straight e to the power of straight y end style close parentheses over denominator straight e to the power of straight y open parentheses 1 plus 2 over straight e to the power of straight y close parentheses end fraction equals limit as straight y rightwards arrow infinity of space fraction numerator open parentheses 1 minus begin display style 2 over straight e to the power of straight y end style close parentheses over denominator open parentheses 1 plus 2 over straight e to the power of straight y close parentheses end fraction equals 1 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight e to the power of negative infinity end exponent equals 0 end style
Answered by Sneha shidid | 17 May, 2019, 09:57: AM
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