Final answer:
To find the derivative of f(x) = (x - 2) / x, you can use either the limit definition of the derivative or the quotient rule. The limit definition involves taking the limit of the difference quotient as h approaches 0, while the quotient rule allows you to find the derivative directly.
Step-by-step explanation:
(a) To find the derivative of the function f(x) = (x - 2) / x using the limit definition of the derivative, we need to find the limit as h approaches 0 of the difference quotient:
lim(h->0) [(f(x + h) - f(x)) / h]
Substituting f(x) = (x - 2) / x and simplifying, we get:
lim(h->0) [(x + h - 2) / (x + h) - (x - 2) / x] / h
After simplifying and taking the limit, we get the derivative of f(x).
(b) To find the derivative of f(x) = (x - 2) / x using the quotient rule, we can express the function as a quotient of two functions: f(x) = (x - 2) * x^-1. Applying the quotient rule, we can find the derivative of f(x).