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- What does the notation $xf(x)$ and $f_{xxx}$ or $f_{xxy}$ mean?
Hi I'm wondering about notations I encountered when studying differential equations and oscillation V′′′ = 3π 4b(fxxx +fxyy +gxxy +gyyy) + 3π 4b2[fxy(fxx +fyy) +gxy(gxx +gyy) +fxxgxx −fyygyy] This is a Calculation of Stability of the limit Cycle in Hopf bifurcation, and I don't know what fxxx etc , means A differential equation is given by dx dt = xf(x, y) What does the xf stand
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- Limit of $\\frac{x^c-c^x}{x^x-c^c}$ as $x \\rightarrow c$
My question is: Show that limx→c xc−cx xx−cc lim x → c x c − c x x x − c c exists and find its value Because the limit is 0 0 I've tried using L'Hopital's rule, but every time I differentiate it I still get 0 0? We're given this hint in the question: use the fact that ab = exp(b log(a)) a b = exp (b log (a)) and I've tried doing this to be able to differentiate and use L'Hopital's
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