Final answer:
To find the derivative using the limit definition, we evaluate the limit of the difference quotient. The limit definition of the derivative is given by f'(x) = lim(h->0) [(f(x+h) - f(x)) / h].
Step-by-step explanation:
To find the derivative using the limit definition, we start by taking the limit as the change in the independent variable approaches zero.
Let's say we have a function f(x) and we want to find its derivative with respect to x.
The limit definition of the derivative is given by:
f'(x) = lim(h->0) [(f(x+h) - f(x)) / h]
We evaluate this limit by plugging in the values of f(x+h) and f(x) for a small value of h and calculate the difference quotient. A
s h approaches zero, we get closer to the instantaneous rate of change of the function at x, which is the derivative.