**Problem:**

Let be a smallest value of the function . Prove that when .

**Proof:**

For ,

.

From this, we see that for and . Consequently, attains its maximum value in the interval . On this interval

So, . But,

As , the first term on the right hand side tends to the limit . In the second term, the factor

of the numerator tends to zero because

.

So,

auf wiedersehen,

Nalin Pithwa.

**Reference: Nordic Mathematical Contest, 1987-2009.**

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