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

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 )

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