Question

Find the derivative using the limit definition of 8/√(x-2)

Answer 1

To find the derivative of 8/√(x-2) using the limit definition, set up the difference quotient, substitute the specific function, and simplify to solve the expression as h approaches 0.

Step-by-step explanation:

To find the derivative of the function f(x) = 8/√(x-2) using the limit definition, we need to apply the formula for the derivative at a point x:

1. Set up the difference quotient: f'(x) = limit as h approaches 0 of [f(x+h) - f(x)]/h
2. Substitute the function f(x) = 8/√(x-2): f'(x) = limit as h approaches 0 of [8/√((x+h)-2) - 8/√(x-2)]/h
3. Simplify and solve the expression under the limit as h approaches 0

The limit definition of a derivative is a fundamental concept in calculus used to calculate the instantaneous rate of change of a function. Through a step-by-step approach, we can determine the derivative of any function using this definition.