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

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 12. limits4 Marks
MCQ
$\mathop {Lim}\limits_{x\,\, \to \,\,\infty } $ $\frac{{2 + 2x + \sin 2x}}{{(2x + \sin 2x){e^{\sin x}}}}$ is :
  • A
    equal to zero
  • B
    equal to $1$
  • C
    equal to $- 1$
  • ✓
    non existent
✓

Answer

Correct option: D.
non existent
d
$\mathop {Limit}\limits_{x\,\, \to \,\,\infty } $$\frac{{\frac{2}{x}\, + \,2\, + \frac{{\sin 2x}}{x}}}{{\left( {2 + \frac{{\sin 2x}}{x}} \right)\,{e^{\sin x}}}}\,$
as $x \Rightarrow \,\,\infty$
$l = \mathop {Limit}\limits_{x\,\, \to \,\,\infty } $ $\frac{2}{{2\,.\,{e^{\sin x}}}}\,$ = oscillatory between $\frac{1}{e}\,$ to $\frac{1}{{{e^{ - 1}}}}\,$ $\Rightarrow$ non existent 

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