# How do you find the equations for the tangent plane to the surface #h(x,y)=cosy# through #(5, pi/4, sqrt2/2)#?

The equation of a plane is

So the tangent plane at any point (x,y,z) is:

we can determine the value of the constant as

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To find the equation for the tangent plane to the surface h(x, y) = cosy through the point (5, π/4, √2/2), we need to calculate the partial derivatives of h(x, y) with respect to x and y at the given point.

The partial derivative of h(x, y) with respect to x is obtained by differentiating h(x, y) with respect to x while treating y as a constant. Similarly, the partial derivative of h(x, y) with respect to y is obtained by differentiating h(x, y) with respect to y while treating x as a constant.

Once we have the partial derivatives, we can use them to construct the equation of the tangent plane. The equation of a plane can be written as:

z - z₀ = ∂h/∂x(x₀, y₀)(x - x₀) + ∂h/∂y(x₀, y₀)(y - y₀)

where (x₀, y₀, z₀) is the given point and ∂h/∂x(x₀, y₀) and ∂h/∂y(x₀, y₀) are the partial derivatives evaluated at that point.

By substituting the values of the given point and the partial derivatives into the equation, we can find the equation of the tangent plane to the surface h(x, y) = cosy through the point (5, π/4, √2/2).

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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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