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Let $f(x)=\frac{e^{\frac{-1}{x}}}{x}$, where $x \in (0, 1)$. Then on $(0, 1)$.

1. $f$ is uniformly continuous.
2. $f$ is continuous but not uniformly continuous.
3. $f$ is unbounded.
4. $f$ is not continuous.
asked in Calculus | 135 views

+1 vote

For interval (0 1), Uniform Distribution Function f(x) defined as 1/(1-0) = 1
i.e. f(x) = 1

So function is NOT Uniformly Distributed.

Lets Check Countinuity,
f(x)=e-1/x/x is everywhere continuous except 0. so it will be Continuous in (0 1).

Value of Function at x=0 is Undefined so it should be UnBounded in (0 1)

B should be correct Choice.

answered by Veteran (48.3k points)