Limit definition of derivative examples

    • [DOC File]DERIVATIVES

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      Definition: The derivative of a function f is the function f ′, defined by. for all x for which this limit exists. The domain of f ′ is the set of all values from the domain of f where the above limit exists. The process of finding the derivative of f is called differentiation of f.

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    • [DOC File]Section 1 - Radford

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      Use the definition of the derivative to find if . Solution: Using the limit definition of the derivative, we see that Example 5: Find the derivative using the definition and use the result to find the equation of the line tangent to the graph of at the point (0, -1). Solution:

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    • [DOC File]MAT 271 .edu

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      Section 2.2 The Derivative. Definition: The derivative of the function at is defined as provided the limit exists. If this limit exists we say that is differentiable at . The general form derivative at every point of , we write the limit definition of derivative . Examples: 1. 2. 3. …

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    • [DOC File]Limits

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      Give a formal definition of derivative as a limit, both at a point and as a function. Give a definition of higher order derivatives, and their interpretation in terms of rates of change. Using the limit definition, calculate derivatives of polynomial functions of degree 3 or less, of rational functions p(x)/q(x) where p and q are polynomials of ...

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    • [DOC File]Calculus 2

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      Using the six examples from above and without using the Limit Definition of the Slope of a Tangent Line, establish some short-cut rules for finding derivatives of functions. Use these rules to find the derivatives (the expression for the slope of a tangent) of the following functions:

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    • [DOCX File]www.utoledo.edu

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      Determine the derivative of a function using the limit definition and derivative theorems. Interpret the derivative as the slope of a tangent line to a graph, the slope of a graph at a point, and the rate of change of a dependent variable with respect to an independent variable.

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    • [DOC File]Tangent Lines and Rates of Change

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      If, at the point , the limit of the slope of the secant line does not exist, then the derivative of the function at this point does not exist either. That is, if , then the derivative also fails to exist as . The following examples show four cases where the derivative fails to exist. At a corner.

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    • [DOC File]Limits - UH

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      Using the new algebra trick again, let’s find the limit as x goes to negative infinity for Popper 08 Question 5 Difference Quotients. En route to the derivative, we’ll start doing Difference Quotients. The formula is. The definition of derivative is. So we’ll be doing this here. f(x + …

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    • [DOC File]Limits – Indeterminate Forms and L’Hospital’s Rule

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      following examples: Example 1: Example 2: [Note: We use the given limit .] Example 3: . [Note: We use the definition. of the derivative where . and a = 8.] Example 4: . [Note: We use the . definition of the derivative where . and .] 1 However, there is a general, systematic method for determining limits with the . indeterminate form .

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