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Part $1$

Use$$ L$\text{'}$H$$pital$\text{'}$s rule to find the limit$.$ Note that in this$$ problem, neither algebraic simplification nor the theorem for limits of rational functions at infinity provides an alternative to$$ L$\text{'}$H$$pital$\text{'}$s rule.

ModifyingBelow lim With x right arrow $1$limx$1$StartFraction $7$ x minus $7$ Over ln x Superscript $8$ EndFraction$7$x$7$lnx$8$

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Part $1$

Select the correct choice$$ and, if$$ necessary, fill in the answer box within your choice.

A$.$

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$($Simplify your$$ answer.$)$

B$.$

The limit does not exist.