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## Homework Statement

The problem is:

A function in the form of f(x)/g(x) is given: [x^2 - pi^2/4 ]/tan^2(x) as x [itex]\rightarrow[/itex] pi/2.

## Homework Equations

## The Attempt at a Solution

Surely I can't solve this question using L'hopital's theorem since it's applicable to indeterminate in the form of 0/0, infinity/infinity, 0 (+- infinity),etc. The above function gives 0/infinity... or am I missing something.. Could I perhaps use trig identity for the denominator ?

Another problem: Also would differentiating [itex]x^{1/x}[/itex]/x-1 as x -> 1 give me an answer of e^1 only ?

Here's how I attempted to solve this problem:

I made y = x^1/x which gave me lny = lnx/x ( which's 0/1) that eventually gives me lny = 1 ? :s

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