12. limits — ગણિત ધોરણ 11 સાયન્સ — Question

$ = y\mathop {\lim }\limits_{n \to \infty } \,\,{\left[ {{{\left( {1 + {{\left( {\frac{x}{y}} \right)}^n}} \right)}^{{{\left( {\frac{y}{x}} \right)}^n}.}}} \right]^{\frac{1}{n}.{{\left( {\frac{x}{y}} \right)}^n}}}$

$ = y{e^0} = y$,

$\left[ {\because \,\,\frac{x}{y} < 1\, \Rightarrow \,\,{{\left( {\frac{x}{y}} \right)}^n} \to 0\,\,{\text{as}}\,\,n \to \infty } \right]$.