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So I use the formula and get . My Maple 13 calculator says this cannot be simplified unless you throw in the limit as h approaches 0, which gets
How does it reach this answer? Thanks to anyone who helps!
Maple 13 calculator (whatever that is) knows squat about good tricks in mathematics: throw it away.
After you simplify the expression for f'(a) within the limit you get:
[Sqrt(a+2) - Sqrt(a+h+2)]/[h*sqrt(a+2)sqrt(a+h+2)] .
Multiply the above by the numerator's conjugate (the same expression as the numerator but with a + sign instead the - one) and simplify. You get an expression perfectly well defined and continuous when h --> 0 and thus you can directly substitute h = 0 and get what you want.
Tonio