Lim X - > 0, the limit of sin (1 / x)? Lim X - > 0, the limit of X * (sin (1 / x))?

Lim X - > 0, the limit of sin (1 / x)? Lim X - > 0, the limit of X * (sin (1 / x))?

The first is unlimited
The second is 0
The first Lim X - > 0 sin (1 / x) = Lim T - > infinite sin (T)
If a is not equal to 0, that is, when t > T0, sin (T) = a, then sin (T + PI) = - A is not equal to a, so the limit does not exist
If the limit is 0, take t = t0 + pi / 2, sin (T) = 1, so a is not zero
The second is because | sin (1 / x)|

Elden Ring Premiere

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