Linearization Flashcard

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What is linear approximation?

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Linear approximation is a method of estimating the value of a function near a point using the tangent line at that point. It is based on the idea that a function can be approximated by a linear function (a straight line) when the input is close to a specific value.

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How do you find the linear approximation of a function at a point?

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What is the maximum area of a rectangular pigpen with 400 ft of fencing next to a wall?

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The maximum area of the rectangular pigpen is achieved with dimensions 100 ft x 200 ft.

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What is the relationship between the dimensions of a rectangle and its area?

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How do you set up an optimization problem for maximum area?

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To set up an optimization problem for maximum area, express the area in terms of one variable, use constraints to eliminate other variables, and then find the critical points by taking the derivative and setting it to zero.

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What is the significance of the tangent line in linear approximation?

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The tangent line at a point on a curve represents the best linear approximation of the curve at that point, providing a way to estimate values of the function nearby.