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STD 11 - 12. limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
The value of $\mathop {Limit}\limits_{x \to \infty } \,\frac{{{{\left( {{2^{{x^n}}}} \right)}^{\frac{1}{{{e^x}}}}}\,\, - \,\,{{\left( {{3^{{x^n}}}} \right)}^{\frac{1}{{{e^x}}}}}}}{{{x^n}}}\,$ (where $n \in N$) is
  • A
    ln $\left( {\frac{2}{3}} \right)$
  • ✓
    $0$
  • C
    $n\,ln \,\left( {\frac{2}{3}} \right)$
  • D
    not defined
✓

Answer

Correct option: B.
$0$
b
$l =\mathop {Limit}\limits_{x \to \infty } \,\frac{{{2^{\frac{{{x^n}}}{{{e^x}}}\,}}\, - \,\,{3^{\frac{{{x^n}}}{{{e^x}}}}}}}{{{x^n}}}\,$             

but $\mathop {Limit}\limits_{x \to \infty } \,\frac{{{x^n}}}{{{e^x}}}\,\, = \,0$ $\Rightarrow l = 0$ 

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