Using the limit definition, how do you find the derivative of # f(x) = (x^21) / (2x3)#?
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To find the derivative of the function ( f(x) = \frac{x^2  1}{2x  3} ) using the limit definition, you would follow these steps:

Start with the definition of the derivative: ( f'(x) = \lim_{h \to 0} \frac{f(x + h)  f(x)}{h} ).

Substitute the given function into the definition: ( f'(x) = \lim_{h \to 0} \frac{\frac{(x + h)^2  1}{2(x + h)  3}  \frac{x^2  1}{2x  3}}{h} ).

Simplify the expression inside the limit by finding common denominators and combining terms.

Once the expression is simplified, evaluate the limit as ( h ) approaches 0 to find the derivative.
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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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