\text { Consider a sequence } f_{n}:[0, \pi] \rightarrow \mathbb{R} \text {, } f_{n}(x)=\left\{\begin{array}{ll} \sin (n x) & 0 \leq x \leq \frac{\pi}{n}, \\ 0 & \frac{\pi}{n} \leq x \leq \pi . \end{array}\right. ) Find pointwise limit of the sequence (fn) on [0, ]. Explain, why fn does not converge uniformly on1 [0, 1].

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