Find the indicated limit$.$ Note that$$ l$\text{'}$H$$pital$\text{'}$s rule may not apply or may require more than one application. Use

minusinfinity

or

infinity

when appropriate.

ModifyingBelow lim With x right arrow infinityStartFraction $2$ e Superscript negative x Over ln left parenthesis $1$ plus $7$ e Superscript negative x Baseline right parenthesis EndFraction

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Part $1$

Select the correct choice below$$ and, if$$ necessary, fill in the answer box to complete your choice.

A$.$

ModifyingBelow lim With x right arrow infinityStartFraction $2$ e Superscript negative x Over ln left parenthesis $1$ plus $7$ e Superscript negative x Baseline right parenthesis EndFractionequalsenter your response here

$($Type an exact answer in simplified$$ form.$)$

B$.$

The limit does not exist.