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    Convergence of the Arctangent Integral

    Homework Statement Is $\intop_{-\infty}^{\infty}\arctan(x)\, dx$ convergent? What about $\lim_{t\rightarrow\infty}\intop_{-t}^{t}\arctan(x)\, dx$? Homework Equations The Attempt at a Solution I think the first integral may actually be divergent the way its written and the second one...
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    Block + Ramp

    Homework Statement A block of m mass slides along a frictionless horizontal surface with a speed of v m/s. After sliding a distance of d, the block makes a smooth transition to a frictionless ramp inclined at an angle of theta ° to the horizontal. The ramp is not fixed to the frictionless...
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    Ruler experiment

    Hello guys. I was doing an experiment on how much a ruler bends at different points when a mass is hung from it. In the experiment, one end is fixed to the table and a mass is hung from the ruler at different points. The relationship seems to resemble a logarithmic curve. Any explanations for this?
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    Ever get the feeling that your door is unlocked?

    Hey guys! I've just thought of a neat idea for a summer project, and I'm requesting some opinions on its usefulness and feasibility. For a forgetful guy like me, I always get the feeling (while I'm walking on the streets) that my door is unlocked. So today I was thinking about how to make...
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    Resistance versus temperature in weak acids, strong acids, and water

    The question below is a rather theoretical one and does not concern any actual calculations. So I have decided to abandon the traditional format. In the past few weeks, I have designed and carried out a lab in which I would test the resistance of a strong acid (0.5 M HCl), a weak acid (0.5 M...
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