Differential Calculus (id: 467a72541)

本题目来源于试卷: Differential Calculus，类别为 IB数学

[填空题]
Consider

$\lim _{x \rightarrow 0} \frac{2 \arctan \left(e^{x}\right)-c}{3 x}$

where $ c \in \mathbb{R}$ .
1. Show that a finite limit only exists for $c=\frac{\pi}{2}$ .   
2. Using l'Hôpital's rule, show algebraically that the value of the limit is $\frac{1}{3}$ .   

参考答案:
空格1: 1.57±2%  空格2: 1/3±2% 


本题详细解析:

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