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(x-h)]/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.

## Answer This Question

## Related Questions

- calculus - f*(x) = lim as h -> 0 [f(x+h)-f(x-h)]/ h write an equation that ...
- Calculus..more help! - I have a question relating to limits that I solved lim(x...
- calculus - State which of the conditions are applicable to the graph of y = f(x...
- Calculus - Find the following limits algebraically or explain why they don’t ...
- Calculus - Can someone provide a function that satisfies all of the following...
- Calculus - 1. a) For the Function and point below , Find f’(a). b) Determine ...
- Calculus - 1. a) For the Function and point below , Find f’(a). b) Determine ...
- calculus - A rational function f(x) contains quadratic functions in both the ...
- Calculus - Give an appropriate answer. Let lim x→6 f(x)=81. Find lim x&#...
- Calculus - determine the absolute extreme values of the function f(x)=sinx-cosx+...

More Related Questions