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    Linearization of a function

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    The distance l from a point at a height h above the Earth's surface to the horizon can be approximated using Pythagoras' theorem by the expression: (Please see the attachment below)

    (a) Find an expression which serves as a linear approximation for l at h=1000 m.

    (b) Give two assumptions you think have been made in deriving the expression above.

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    Solution Preview

    Please see the attachment below for the complete solution.

    The above equation can be written in a more useful form as:

    l = (h^2+2rh)^1/2

    Taking the derivative of l with respect to h gives:

    dl/dh = ...

    Solution Summary

    This shows how to perform linearization of a function related to the Pythagorean theorem. Two assumptions for deriving the expressions are provided.