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Tangent Planes and Linear Approximations. Tangent Planes Rearranging terms:

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Presentation on theme: "Tangent Planes and Linear Approximations. Tangent Planes Rearranging terms:"— Presentation transcript:

1 Tangent Planes and Linear Approximations

2 Tangent Planes Rearranging terms:

3 Tangent Plane Example Simplifying: Zoom in The paraboloid and its tangent plane at P:

4 Linear Approximation

5 Linear Approximation - Example

6 Differentials

7 Differentials Example (a) (b) Actual value:

8 Differentials 3D -Example Let x, y and z be the dimensions of the box. The dimensions of a rectangular box are measured to be 70 cm, 55 cm and 30 cm and each measurement is correct to within 0.1 cm. Use differentials to estimate the largest possible error when the surface area of the box is calculated from these measurements.


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