# How do you use the limit definition to find the slope of the tangent line to the graph # f(x) = x^2#?

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To use the limit definition to find the slope of the tangent line to the graph of f(x) = x^2, we can follow these steps:

- Choose a point on the graph of f(x) = x^2, let's say (a, f(a)).
- Choose a second point on the graph that is close to (a, f(a)), let's say (a + h, f(a + h)).
- Calculate the slope of the secant line passing through these two points using the formula: (f(a + h) - f(a)) / (a + h - a).
- Simplify the expression: (f(a + h) - f(a)) / h.
- Take the limit as h approaches 0 of the expression obtained in step 4.
- The resulting limit will give us the slope of the tangent line to the graph of f(x) = x^2 at the point (a, f(a)).

By following these steps, we can find the slope of the tangent line to the graph of f(x) = x^2 using the limit definition.

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