Evaluate the Limit

Problem

(lim_h→0)((ƒ*(x+h)−ƒ(x))/h)

Solution

1. Identify the expression as the formal definition of the derivative of a function ƒ(x) with respect to x

2. Recognize that this limit represents the instantaneous rate of change of the function at any point x

3. Assign the standard notation for this limit, which is ƒ(x)′ or d(ƒ(x))/d(x)

Final Answer

(lim_h→0)((ƒ*(x+h)−ƒ(x))/h)=ƒ(x)′

Want more problems? Check here!