Final answer:
The limit of 10xe^1 / (x - 10x) as x approaches infinity simplifies to -10/9 e. L'Hospital's Rule is not needed for this expression.
Step-by-step explanation:
The student is asking to evaluate the limit of the expression 10xe^1 / (x - 10x) as x approaches infinity. Applying L'Hospital's Rule is a common method for finding the limit of a function when the direct substitution leads to an indeterminate form like 0/0 or ∞/∞. However, in this case, there seems to be a typo in the original question - the correct form may be 10xe^(1/x) / (x - 10x) or a similar expression where L'Hospital's Rule would apply.
The expression given 10xe^1 / (x - 10x) does not require L'Hospital's Rule, as the denominator simplifies directly to -9x, which leads to the limit being -10/9 e as x approaches infinity. If the intended problem is indeed 10xe^(1/x) / (x - 10x), we should first simplify the denominator to -9x and then apply L'Hospital's Rule if necessary, which in this case, after simplifying, it isn't required either.