题目
题目

MAT135H5_F25_ALL SECTIONS 4.8 Preparation Check

多重下拉选择题

Let's evaluate the following limit: lim 𝑥 → 1 sin ⁡ ( 𝜋 𝑥 ) 𝑥 − 1   Can l'Hopital's rule be used to evaluate the limit? [ Select ] Yes No This limit is an indeterminate form of type [ Select ] infinity/infinity 0/0 It's not an indeterminate form 0^0 1^infinity infinity - infinity . The final answer is [ Select ] -pi pi/2 -1 0 pi 1 . 

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标准答案
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思路分析
First, restating the problem: we are evaluating the limit as x approaches 1 of sin(π/x) divided by (x − 1), and we are given three dropdown decisions to fill: whether L'Hôpital's rule can be used, what indeterminate form arises, and what the final value is. Option 1 discussion (Can L'Hôpital's rule be used?): The limit has a numerator sin(π/x) and a denominator x − 1. As x → 1, the numerator tends to sin(π) = 0 and the denominator tends to 0, giving......Login to view full explanation

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