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Please solve the question in attachment. ... .. ... ..ANS is 1/√e......... .....

Please solve the question in attachment. ... .. ... ..ANS is 1/√e......... ..... 

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Grade:12th pass

2 Answers

Aditya Gupta
2081 Points
5 years ago
call the limit L.
then logL= lim [{log(1+x)}/x – 1]/x
now use series of log(1+x)= x – x^2/2+O(x^3)
so logL= lim [1 – x/2+O(x^2) – 1]/x
= – ½
so L= e^(–½ )
L=  1/√e
Aditya Gupta
2081 Points
5 years ago
Note above that we could also use l hospital rule, but sometimes the question becomes 10 times easier when we simply use series expansion. I am giving this advice because there are some classic examples in TMH which are impossible to solve using l hospital rule and can only be solved using series expansion! So it is always advisable to remember all the important series expansions

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