Use the definition of the derivative to evaluate each limit. a. limh →0 (e^h-1)/(h) b. limh →0 (

step 1 I like to just think of the limit definition of the derivative, may I should write out. F prime

Use the definition of the derivative to evaluate each limit....

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Key Concepts

Definition of the Derivative

The definition of the derivative involves computing the limit of the difference quotient, which is given by f'(x) = lim??0 [f(x+h) - f(x)]/h. This concept is essential because it provides the fundamental method for calculating the instantaneous rate of change or the slope of the tangent line of a function at a point.

Exponential Function and its Derivative

The exponential function, commonly expressed as e^x, has a unique property where its derivative is the function itself, that is, d/dx e^x = e^x. This characteristic is pivotal when applying the definition of the derivative to exponential functions, as it simplifies the limit evaluation process and underscores the natural growth behavior of the function.

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