What is the Correct Method for Evaluating Limits?

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The discussion revolves around evaluating limits in a mathematical context. The user initially attempted to calculate a limit by substituting values but arrived at an incorrect answer. They expressed confusion over their calculation process, suspecting a mistake in using the calculator. The correct evaluation method involves careful substitution and simplification of the expression. Ultimately, the user seeks clarification on the proper approach to limit evaluation.
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Homework Statement


http://img517.imageshack.us/img517/5817/96728501it3.jpg



The Attempt at a Solution


I plugged in the values 1 and -4 and got

6(-4)-1 / 3+1

equals -7.333. But got the question wrong. What am I doing wrong?
 
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(6*-4 - 1)/4= - 6.25
 
Must of put it into my calculator wrong..Thanks
 
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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