# How do I calculate the upper bound of a rectangle?

I will assume that you mean "How do I calculate the upper bound of a function over a rectangle?".

The upper bound will be the maximum value of the function, occurring at one of the following locations:

(2) Along a horizontal edge, where the partial derivative is zero:

(3) Along a vertical edge, where the partial derivative is zero:

(4) Inside the body of the rectangle at a point where both partial derivatives are zero:

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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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