# What is the total differential of #z=x^2+2y^2-2xy+2x-4y-8#?

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The total differential of (z = x^2 + 2y^2 - 2xy + 2x - 4y - 8) is given by:

[dz = \frac{\partial z}{\partial x} dx + \frac{\partial z}{\partial y} dy]

Where:

[\frac{\partial z}{\partial x} = 2x - 2y + 2] [\frac{\partial z}{\partial y} = 4y - 2x - 4]

Therefore, the total differential is:

[dz = (2x - 2y + 2) dx + (4y - 2x - 4) dy]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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