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CBSE Class 11-science Answered

E v a l u a t e space limit as x rightwards arrow 0 of fraction numerator e to the power of begin display style 1 over x end style end exponent over denominator e to the power of begin display style 1 over x end style end exponent plus 1 end fraction


Please provide solution to this question
Asked by Topperlearning User | 16 Nov, 2016, 04:33: AM
answered-by-expert Expert Answer

L e t space u s space c a l c u l a t e space t h e space l e f t space h a n d space l i m i t
limit as x rightwards arrow 0 to the power of minus of fraction numerator e to the power of begin display style 1 over x end style end exponent over denominator e to the power of begin display style 1 over x end style end exponent plus 1 end fraction equals limit as x rightwards arrow 0 to the power of minus of fraction numerator 1 over denominator 1 plus e to the power of negative begin display style 1 over x end style end exponent end fraction
equals limit as h rightwards arrow 0 of fraction numerator 1 over denominator 1 plus e to the power of begin display style 1 over h end style end exponent end fraction
equals 0
R i g h t space h a n d space l i m i t space
limit as x rightwards arrow 0 to the power of plus of fraction numerator e to the power of begin display style 1 over x end style end exponent over denominator e to the power of begin display style 1 over x end style end exponent plus 1 end fraction equals limit as x rightwards arrow 0 plus of fraction numerator 1 over denominator 1 plus e to the power of negative begin display style 1 over x end style end exponent end fraction
equals limit as h rightwards arrow 0 of fraction numerator 1 over denominator 1 plus e to the power of begin display style negative 1 over h end style end exponent end fraction
equals 1
L H L not equal to R H L space s o space t h e space l i m i t space d o e s n apostrophe t space e x i s t

Answered by | 16 Nov, 2016, 06:33: AM
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