Lim _ x , , , , 2 + 2x + 2x (2x + 2x) e^ x is : - Vidyadip

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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