Find the linear approximation of the function f (x) = √16-x at a = 0 and use it to approximate the numbers √15.9 and √15.99.

L (x) = f (a) + f' (a) (x - a); where f (x) = sqrt (16 - x) and a = 0.

f' (x) = - 1 / (2sqrt (16 - x)),

f' (0) = - 1 / (2sqrt (16 - 0)) = - 1 / (2sqrt (16)) = - 1/2 (4) = - 1/8,

f (0) = sqrt (16 - 0) = sqrt (16) = 4

L (x) = 4 - 1/8 (x - 0) = 4 - 1/8x.

sqrt (15.9) = sqrt (16 - 0.1) = 4 - 1/8 (0.1) = 4 - 0.0125 = 3.9875

sqrt (15.99) = sqrt (16 - 0.01) = 4 - 1/8 (0.01) = 4 - 0.00125 = 3.99875