Question

[3011311129 (A) - 7 (where { } denotes the fractional part of x) is equal to (B) e2-8 (C) 62 - 6 (D) None of these

JEE/Engineering Exams

Maths

Solution

4.0 (1 ratings)

( operatorname{li}_{x rightarrow 0}left{(1+x) frac{2}{x}right} ) ( y=lim _{x rightarrow 0}left{(1+x)^{frac{2}{x}}right} ) ( Rightarrow log y=operatorname{lif}_{x rightarrow 0}left(frac{2}{x} log (1+x)right} ) ( Rightarrow log _{7}=operatorname{li}_{x rightarrow 0}left{frac{2}{x}left(x-frac{x^{2}}{2}+frac{x^{3}}{3}-xright)right} ) ( Rightarrow log y=lim _{x rightarrow 0}left{2left(1-x_{2}+frac{x^{2}}{3}--1right)right} ) ( Rightarrow quad y=e^{u_{1}} x_{0}^{12} ) ( =e^{2-[2]}=e^{2 cdot 2}=e^{0} ) Option ( frac{=1}{E} )