# How do you use the limit definition to find the slope of the tangent line to the graph #f(x)=9x-2 # at (3,25)?

the slope of the tangent is

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To find the slope of the tangent line to the graph of f(x) = 9x - 2 at (3,25) using the limit definition, we can follow these steps:

- Start with the given function f(x) = 9x - 2.
- Determine the equation of the tangent line by finding the derivative of f(x).
- Take the derivative of f(x) using the power rule, which states that the derivative of x^n is n*x^(n-1).
- Applying the power rule, the derivative of 9x - 2 is 9.
- The derivative of f(x) is the slope of the tangent line at any point on the graph.
- Evaluate the derivative at x = 3 to find the slope at that specific point.
- Substituting x = 3 into the derivative, we get the slope of the tangent line as 9.
- Therefore, the slope of the tangent line to the graph of f(x) = 9x - 2 at (3,25) is 9.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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