Answer:
L(997) = 0.001003
Step-by-step explanation:
L(x) = f(a) + f'(a)(x-a)
f'(x) = [tex]\frac{-1}{x^2}[/tex]
a = 1000
x = 997
L(997) = f(1000) + f'(1000)(997-1000)
L(997) = (1/1000) + (-1/(1000^2))*(-3)
L(997) = [tex]\frac{1}{1000}[/tex] + [tex]\frac{3}{1000000}[/tex]
L(997) = 0.001003
