How do you use the limit definition to find the slope of the tangent line to the graph #f(x)=(3x1)/(x1)# at x=0?
Please see below.
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To find the slope of the tangent line to the graph of f(x)=(3x1)/(x1) at x=0 using the limit definition, we can follow these steps:

Start with the equation of the function: f(x) = (3x1)/(x1).

Determine the equation of the tangent line. The slope of the tangent line is equal to the derivative of the function at the given point.

Find the derivative of f(x) using the limit definition. The derivative of f(x) is given by the limit as h approaches 0 of [f(x+h)  f(x)]/h.

Substitute the given value of x=0 into the derivative expression obtained in step 3.

Simplify the expression and evaluate the limit as h approaches 0.

The resulting value will be the slope of the tangent line to the graph of f(x) at x=0.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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