TIFR-2015-Maths-A-8

Question

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

• A. $f$ is uniformly continuous.
• B. $f$ is continuous but not uniformly continuous.
• C. $f$ is unbounded.
• D. $f$ is not continuous.

Answer 1

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.

Comments

Can you please elaborate Uniform distribution statement