How Do You Solve the Limit Involving Tangent and Sine Functions?

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The limit in question is expressed as lim_{x → π/4} (√[3]{tan(x)} - 1) / (2sin²(x) - 1). It is noted that the expression involves an indeterminate form of 0/0, making L'Hopital's Rule a suitable method for evaluation. There is some confusion regarding the notation "tgx," which is clarified to mean tan(x). Using L'Hopital's Rule will help simplify the limit and find the solution. The discussion emphasizes the importance of proper notation in mathematical expressions.
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Homework Statement


\lim_{x \rightarrow \frac{\pi}{4}} \frac{\sqrt[3]{tgx} - 1}{2sin^2x-1}

Homework Equations


The Attempt at a Solution


I don't even know where to begin
 
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abruski said:

Homework Statement


\lim_{x \rightarrow \frac{\pi}{4}} \frac{\sqrt[3]{tgx} - 1}{2sin^2x-1}


Homework Equations





The Attempt at a Solution


I don't even know where to begin

Does tgx mean tan(x)? If that's what is meant, tgx is very unclear.

Assuming that tan(x) is what we're dealing with, the limit has the indeterminate form [0/0], so L'Hopital's Rule is applicable.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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