Monday 16 August 2021

Let \[f(x)=e^{-|x|}, x \in \mathbb{R}\] and \[g(\theta)=\int_{-1}^{1} f\left(\frac{x}{\theta}\right) d x, \theta \neq 0\] Then, \[\lim _{\theta \rightarrow 0} \frac{g(\theta)}{\theta}=\]

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Define \(f: \mathbb{R} \rightarrow \mathbb{R}\) by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, &a...