Posted by Anonymous on Monday, October 29, 2007 at 2:53pm.
For a function f, let f*(x) = lim as h→0 be [f(x+h)  f(xh)]/h
a) Determine f*(x) for f(x) = cosx
b) write an equation that expresses the relationship between the functions f* and f` where f` denotes the usual derivative of f

calculus  drwls, Monday, October 29, 2007 at 3:20pm
Use the trigonometric identity
cos (x + h) = cosx cosh  sinx sinh
This means that
cos(x + h)  cosx
= (cosh 1) cosx  sin x sinh
For very small h, sin h = h and cos h = 1, so [cos(x + h)  cosx]/h > sin x
sin x is the exact derivative of cos x.
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