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Lazy Lulu is looking at this limit:  and does not want to calculate it using algebra. Lulu recognizes this limit as a definition of the derivative at a point. She thinks she can use the Power Rule instead.

  1. What variation of the definition of the derivative is this?

    This is Ana's Definition of the Derivative:

  2. What is the equation of ? What is the value of ?

    Observe that when .

    Notice that , which confirms that equation of is correct.

  3. Use the Power Rule to write an equation for and then use it to calculate .

    You just avoided a lot of Algebra!