_ x 0 , ( mx)^ n/ x^2 equals - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 0} \,{(\cos mx)^{n/{x^2}}}$ equals

A
${e^{\frac{{{m^2}n}}{2}}}$
✓
${e^{\frac{{{-m^2}n}}{2}}}$
C
${e^{ - {m^2}n}}$
D
${e^{\frac{{{m}n}}{2}}}$

✓

Answer

Correct option: B.

${e^{\frac{{{-m^2}n}}{2}}}$

b
$\mathop {\lim }\limits_{x \to 0} {\left( {\cos mx} \right)^{n/{x^ - }}}\left( {{1^\infty }form} \right)$

${e^{\mathop {\lim }\limits_{x \to 0} \left( {\cos mx - 1} \right) \times \frac{n}{{{x^2}}}}}$

${e^{\mathop {\lim }\limits_{x \to 0} \frac{{ - \left( {1 - \cos mx} \right)n}}{{{x^2}}}}}$

${e^{ - \frac{{{m^2}}}{2} \times n}}$

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