MCQ
If $0 < x < y$ then $\mathop {\lim }\limits_{n \to \infty } {({y^n} + {x^n})^{1/n}}$ is equal to
- A$e$
- B$x$
- ✓$y$
- DNone of these
$ = 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$,
$\left[ {\because \,\,\frac{x}{y} < 1\, \Rightarrow \,\,{{\left( {\frac{x}{y}} \right)}^n} \to 0\,\,{\text{as}}\,\,n \to \infty } \right]$.
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