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Levitating Disk

I think the black object is made of superconducting material which works as superconductor at a temperature above the temperature of the liquid Nitrogen (B.P. -196°C). The disk is a magnet. When the magnet is moved towards the black object it causes eddy currents in it due to induction which die down soon due to the internal resistance when liquid Nitrogen in not poured. However, when liquid Nitrogen is poured the temperature falls and falls enough for the black object to behave like a superconductor. Now, when the magnet is moved causing eddy currents then they don't die down quickly and the magnetic field produced by them opposes the magnet (disc) by Lenz's law and the magnet hangs.

This phenomenon looks different from that of the levitating frog which is due to the diamagnetism.

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$f(x)=x^6+2x^4+x^3+2x+3 $

$\mathop {\lim }\limits_{x \to 1} \frac{{{x^n}f(1) - f(x)}}{{x - 1}} = 44$


Let $f(x)=x^6+2x^4+x^3+2x+3,x \in R $. Then the natural number n for which $\mathop {\lim }\limits_{x \to 1} \frac{{{x^n}f(1) - f(x)}}{{x - 1}} = 44$ is _ _ _ _ . Solution Since the limit has $\left[ {\frac{0}{0}} \right]$ form, L.H. Rule is applicable. Thus, $\mathop {\lim }\limits_{x \to 1} n{x^{n - 1}}f(1) - f'(x) = 44$ $\therefore nf(1) - f'(1) = 44$ $\therefore n.9 - ({6.1^5} + {8.1^3} + {3.1^2} + 2.1) = 44$ $ \Rightarrow 9n - 19 = 44$ $\Rightarrow n=7$