grandes-ecoles 2018 Q26

grandes-ecoles · France · centrale-maths1__pc Connected Rates of Change Pointwise Limit of a Difference Quotient

Let $t \in \mathbb{R}_{+}^{*}$ and $x \in\ ]0,1[$. Show that $\lim_{h \rightarrow 0} \frac{f(t, x+h) - 2f(t, x) + f(t, x-h)}{h^{2}} = \frac{\partial^{2} f}{\partial x^{2}}(x, t)$.

Let $t \in \mathbb{R}_{+}^{*}$ and $x \in\ ]0,1[$. Show that $\lim_{h \rightarrow 0} \frac{f(t, x+h) - 2f(t, x) + f(t, x-h)}{h^{2}} = \frac{\partial^{2} f}{\partial x^{2}}(x, t)$.

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