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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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