Q.The function $f(x) = \begin{cases} \frac{x \sin(\pi x)}{\pi} & x \text{ integer} \ 0 & \text{otherwise} \end{cases}$ is continuous at

all integers

no integers

only at

x=0

everywhere

The correct solution involves applying the fundamental concept to derive the final value step by step...

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Q.The function f(x)={xsin⁡(πx)πx integer 0otherwisef(x) = \begin{cases} \frac{x \sin(\pi x)}{\pi} & x \text{ integer} \ 0 & \text{otherwise} \end{cases}f(x)={πxsin(πx)​​x integer 0​otherwise​ is continuous at