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The derivative of a function, f(x) is equal to lim h->0 f(x+h)-f(x) / h. True or...

The derivative of a function, f(x) is equal to lim h->0 f(x+h)-f(x) / h. True or false. please explain.

Math   Calculus   
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Answer #1

The definition is True.

Let's try to understand the limit definition of a derivative.

A derivative is defined as the change of y in a function with respect to a change in x. (in simple words)

Considering the fact that function is differentiable, it must be continuous. Let's consider a continuos function like this:I tried making this image to help you understand it better. Thanks!

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