# How do you compute the gradient of the function #p(x,y)=sqrt(24-4x^2-y^2)# and then evaluate it at the point (-2,1)?

By making both terms simpler, we can get

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To compute the gradient of the function p(x, y) = sqrt(24 - 4x^2 - y^2), we need to find the partial derivatives with respect to x and y.

The partial derivative with respect to x (denoted as ∂p/∂x) can be found by differentiating the function with respect to x while treating y as a constant.

∂p/∂x = (-8x) / (2 * sqrt(24 - 4x^2 - y^2))

The partial derivative with respect to y (denoted as ∂p/∂y) can be found by differentiating the function with respect to y while treating x as a constant.

∂p/∂y = (-2y) / (2 * sqrt(24 - 4x^2 - y^2))

To evaluate the gradient at the point (-2, 1), substitute x = -2 and y = 1 into the partial derivatives:

∂p/∂x = (-8 * -2) / (2 * sqrt(24 - 4(-2)^2 - 1^2)) ∂p/∂y = (-2 * 1) / (2 * sqrt(24 - 4(-2)^2 - 1^2))

Simplifying these expressions will give you the values of the partial derivatives at the given point.

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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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