Question

use the limit definition on page 3-2 of this lab to find f'(8) where f (x) = 1/x_5 clearly show every step in evaluating this limit.

Answer 1

To find f'(8) for f(x) = 1/x^5, use the limit definition of the derivative and simplify the expression.

Step-by-step explanation:

To find the derivative of f(x) = 1/x^5 at x = 8, we can use the limit definition of the derivative. The limit definition states that f'(a) is equal to the limit as h approaches 0 of (f(a + h) - f(a))/h. Let's plug in the values into the formula:

f'(8) = lim(h->0) [(1/(8 + h)^5 - 1/8^5)/h]

Next, let's simplify the expression:

Apply the limit as h approaches 0.