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Soit \(f : {\R^3} \to \R\) de classe \(\mathcal{C}^1\) telle que \(f(0,1,1) = 0\), \(\frac{\partial f}{\partial x}(0,1,1) = 1\), \(\frac{\partial f}{\partial y}(0,1,1) = 2\), \(\frac{\partial f}{\partial z}(0,1,1) = 3\).
Peut-on déterminer \(\lim_{t\to0} \frac{f(t^2,\ch t,e^t)}{f(t,\cos t,\ch t)}\) ?