A Definite integral where solution. involves infinity - infinity

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The discussion focuses on evaluating a definite integral that involves an indeterminate form of infinity minus infinity. Participants suggest starting by evaluating the integral with limits from 0 to b and then taking the limit as b approaches infinity. The use of partial fractions is recommended as a method for solving the integral. There is a mention of issues with posting images, leading to confusion in the thread. Overall, the conversation emphasizes the importance of proper limit handling and algebraic manipulation in solving the integral.
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What work have you done on this? What makes you think that it is of the indeterminate form in the thread title?

When you start in on this, if you haven't done so already, look at the integral with limits of integration 0 and b, do the integration, and then take the limit as b approaches infinity.

In doing the integral, I would go at this using partial fractions.
 
See my reply in the other thread.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

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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