## theEric 3 years ago Hi! I'm trying to use the following equation in calculus 3:$\Delta z = dz + \epsilon _1 \Delta x + \epsilon _2 \Delta y$ I know the value of dz, and the problem states that $\lim_{\Delta x \rightarrow 0}$and$\lim_{\Delta y \rightarrow 0}=0$ Then is$\Delta z = dz$? Full question, after being given z: Find the increment $\Delta z = f(x+\Delta x, y + |delta y) - f(x,y)$ in the form of $\Delta z = dz + \epsilon _1 \Delta x + \epsilon_2\Delta y$, where $\epsilon_1$ and $\epsilon_2$have limits 0 as$(\Delta x, \Delta y) \rightarrow (0,0)$.

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