Linearization of a function. Attachments in Word.

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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...h+r)

Plugging the above equations into the Euler Equation above:

lh=1000 = (0^2+2r(0))^1/2+[(0^2+2r(0))^-1/2(0+r)](1000-0)

Simplify,

lh=1000 = 1000r

This is the linear approximation to the original ...