How do you use the limit definition to find the slope of the tangent line to the graph #y=1x^3# at x=2?
So,
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To find the slope of the tangent line to the graph y=1x^3 at x=2 using the limit definition, we can follow these steps:

Start with the equation of the graph: y = 1  x^3.

Determine the derivative of the function y with respect to x, denoted as dy/dx or f'(x). In this case, the derivative is f'(x) = 3x^2.

Substitute the given xvalue, x=2, into the derivative function to find the slope at that point: f'(2) = 3(2)^2 = 12.

The slope of the tangent line to the graph y=1x^3 at x=2 is 12.
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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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