题目
题目

MTH1030 -1035 - S1 2025 MTH1030/35 Week 7 lesson quiz: L’Hôpital’s rule

单项选择题

What is \[\lim_{x\to \infty} \left (1+\frac{1}{x}\right )^{-x}?\]

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标准答案
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思路分析
The prompt presents a limit question and indicates answer choices, but the provided data shows that the list of answer options is missing (the answer_options array is empty), while the answer field contains a single option: a. 1/e. First, restating the question: What is lim_{x -> ∞} (1 + 1/x)^{-x} ? This asks for the value of a classic indeterminate-looking expression as x grows without bound. Now, evalua......Login to view full explanation

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Find the limit    

NOTE: Due to formatting constraints, limits are shown with a horizontal bar in these quiz questions.For example: will be written as: \( \frac{lim}{x \rightarrow a }f(x) \)Solve the following limit and write your answer to three decimal places.\( \frac{lim}{x \rightarrow 2 } (\frac{x^3+7x^2-18x}{x^2-4}) \)

NOTE: Due to formatting constraints, limits are shown with a horizontal bar in these quiz questions.For example: will be written as: \( \frac{lim}{x \rightarrow a }f(x) \)Solve the following limit and write your answer to three decimal places.\( \frac{lim}{x \rightarrow \infty } (\frac{2x^2+4x+-6}{-2x^2+-7x+10}) \)

NOTE: Due to formatting constraints, limits are shown with a horizontal bar in these quiz questions.For example: will be written as: [math: limx→af(x)] \frac{lim}{x \rightarrow a }f(x) Solve the following limit and write your answer to three decimal places.[math: limx→2(x3+7x2−18xx2−4)] \frac{lim}{x \rightarrow 2 } (\frac{x^3+7x^2-18x}{x^2-4})

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