How to find $$\lim_{x\to 0}\frac{\sin\tan x-\tan\sin x}{7x^7}?$$
L’Hopital rule does not work because derivative of numerator goes very wide and I need to take 7? Can somebody show me other way of finding it?
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Taylor expand $\sin(\tan x)$ and $\tan(\sin x)$ out to order $x^7$. The first six orders will match; the difference is then $kx^7$ and your answer is $k/7$. – Mark Fischler Dec 11 '17 at 14:14
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It reminds me somehow the old Arnold's problem. – A.Γ. Dec 11 '17 at 14:21
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1the solution should be $$-\frac{1}{210}$$ – Dr. Sonnhard Graubner Dec 11 '17 at 14:27