How do you use the limit definition to find the slope of the tangent line to the graph #f(x)= 2xx^2# at x=0?
The slope of the tangent when
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To find the slope of the tangent line to the graph of f(x) = 2x  x^2 at x = 0 using the limit definition, we can follow these steps:

Start with the equation of the function: f(x) = 2x  x^2.

Determine the equation of the tangent line. The equation of a line can be written as y = mx + b, where m represents the slope of the line. We need to find the slope (m) of the tangent line.

Use the limit definition of the derivative to find the slope. The derivative of a function f(x) at a specific point x = a can be defined as the limit of the difference quotient as h approaches 0. The difference quotient is given by [f(a + h)  f(a)] / h.

Substitute the values into the difference quotient. In this case, a = 0. So, we have [f(0 + h)  f(0)] / h.

Simplify the expression. Substitute the function f(x) = 2x  x^2 into the difference quotient and simplify the numerator.

Take the limit as h approaches 0. Evaluate the expression as h approaches 0 to find the slope of the tangent line.

The resulting value will be the slope of the tangent line to the graph of f(x) = 2x  x^2 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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