To find the derivative of a function using the limit definition, replace the variable x with (a + h) in the function, substitute the value of f(a), and then evaluate the limit as h approaches zero; for example, when f(x) = x² and a = 1, you replace x with (1 + h) and f(a) with 1, then compute the limit as h approaches zero.
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Derivatives Using the Limit Definition | Practice Problems | Calculus 1Added:
So, we basically do is we have this function over here, x squared, right?
So, here f of a that that is our one and our point a is equals to one. Okay, so we're simply going to replace it with 1 + h 1 f of 1. So, because we have to replace it with f of a and our f of a happens to be this is a and this is f of a. This happens to be one, okay? So, we simply have to replace it by one.
And next we have an h, so limit as x approaches zero. So, now we basically have to every time we see an x here in inside the function, we need to replace it with 1 + h.
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