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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to \infty } {\left[ {1 + \frac{1}{{mx}}} \right]^x}$ equal to
  • ✓
    ${e^{1/m}}$
  • B
    ${e^{ - 1/m}}$
  • C
    ${e^m}$
  • D
    ${m^e}$
✓

Answer

Correct option: A.
${e^{1/m}}$
a
(a) Let $y = \mathop {\lim }\limits_{x \to \,\infty } \,{\left( {1 + \frac{1}{{mx}}} \right)^x} = \mathop {\lim }\limits_{x \to \,\infty } \,{\left( {1 + \frac{1}{{mx}}} \right)^{mx \cdot \frac{1}{m}}}$

$ \Rightarrow \,\,y = {e^{1/m}},\,\,\,\left( {\because \mathop {\lim }\limits_{x \to \,\infty } \,{{\left( {1 + \frac{1}{x}} \right)}^x} = e} \right)$

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