# Linearization of a function

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.

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