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Asked by g_archanasharma | 02 Mar, 2019, 19:36: PM
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begin mathsize 12px style limit as x rightwards arrow open square brackets a close square brackets of fraction numerator e to the power of open curly brackets x close curly brackets end exponent minus open curly brackets x close curly brackets minus 1 over denominator open curly brackets x close curly brackets squared end fraction space........... left parenthesis 1 right parenthesis w h e n space x rightwards arrow left square bracket a right square bracket comma space t h e n space open curly brackets x close curly brackets space rightwards arrow 0 space space comma space b e c a u s e space open curly brackets x close curly brackets space i s space f r a c t i o n space p a r t space o f space x space equals space left square bracket x right square bracket plus open curly brackets x close curly brackets l e t space u s space u s e space t h e space s u b s t i t u t i o n space u space equals space open curly brackets x close curly brackets t h e n space e x p r e s s i o n space left parenthesis 1 right parenthesis space i s space w r i t t e n space a s space comma space space space space space limit as u rightwards arrow 0 of fraction numerator e to the power of u minus u minus 1 over denominator u squared end fraction space equals space limit as u rightwards arrow 0 of space 1 over u squared space open parentheses 1 plus u space plus u squared over 2 space plus space t e r m s space o f space u cubed space a n d space h i g e r space o r d e r s space space minus space u space minus 1 close parentheses equals space limit as u rightwards arrow 0 of space open parentheses 1 half plus space t e r m s space o f space u space a n d space h i g h e r space o r d e r close parentheses space equals space 1 half end style
Answered by Thiyagarajan K | 03 Mar, 2019, 11:24: AM

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