Calculus/derivative

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Expert: Scotto - 7/15/2008


Question
The fundamental concept of the derivative is convergence to a limit..ie an unknown value can be measured by closing in on it thru approximations that get finer and finer.I cannot understand what it means..can you help me with an example?

Answer
If you had a simple function, for example, f(x)=x+2 for all x>0, then f(0) would not be defined.  The limit, though, as x approaches 0 is 2,

It all comes down to an epsilon-delta proof.  The variable delta is for the y error and the variable epsilon is for the x error.  No matter how small of a delta error is given, an epsilon can be found to make it true.

For the problem given, the limit as x approaches 0 of the function x+2 = 2, even though at 0, the function was not defined.

Or lets take the function f(x)=(x²-1)/(x+1).  At x=-1, the function is undefined since we have 0/0.  The limit x at approaches -1, though can be shown to be -2.  The function looks like a line x-1 with a whole at x=-1, but it does have a limit as x approaches -1.

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Scotto

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

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