lim n-> infinity (cos(4*x/(n^.5)))^n I can plug this into mathematica and get e^-(8*x^2) but I don't know how that answer was obtained...
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Originally Posted by soma lim n-> infinity (cos(4*x/(n^.5)))^n I can plug this into mathematica and get e^-(8*x^2) but I don't know how that answer was obtained... Note that Let . Applying natural log to both sides gives us Now apply L'Hôpital's rule. Can you try to take it from here?
For L'Hôpital's rule, I derived the top and bottom and got 0/0 again, and the second derivative looks daunting. Can you help me further with this?
Originally Posted by Chris L T521 Note that Let . Applying natural log to both sides gives us Now apply L'Hôpital's rule. Can you try to take it from here? Originally Posted by soma For L'Hôpital's rule, I derived the top and bottom and got 0/0 again, and the second derivative looks daunting. Can you help me further with this? After applying L'Hôpital's rule once, we have Applying it another time, we see that Therefore, Does this make sense? (Note that when we differentiated, it was with respect to , not ).
Perfect! It took me a while to compute those derivatives myself, but I see how it all fits together now. Thanks so much!
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