QJEEM16Mae822: JEE Main 2016 Mathematics - Class 12 JEEM16Mae822 Solution: If    then 'a' is equal to :

Question

Verified Solution • 2025–26 Session moderate

If

\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} - {4 \over {{x^2}}}} \right)^{2x}} = {e^3},

then 'a' is equal to :

Accepted Answer

Given,

\mathop {\lim }\limits_{x \to \propto } {\left( {1 + {a \over x} - {4 \over {{x^2}}}} \right)^{2x}} = {e^3}

So,

\mathop {\lim }\limits_{x \to \propto } {\left( {1 + {a \over x} - {4 \over {{x^2}}}} \right)^{2x}}\,\left[ {{1^ \propto }\,\,\,form} \right]

= {e^{\mathop {\lim }\limits_{x \to \propto } \left[ {\left( {1 + {a \over x} - {4 \over {{x^2}}} - 1} \right)2x} \right]}}

= {e^{\mathop {\lim }\limits_{x \to \propto } \left( {2a - {8 \over x}} \right)}}

= {e^{2a}}

\therefore

e^2a = e³

\therefore

2a = 3

\Rightarrow

a

=

{3 \over 2}

QJEEM16Mae822: JEE Main 2016 Mathematics - Class 12 JEEM16Mae822 Solution: If &nbsp;&nbsp; then 'a' is equal to :