Hey guys, here's another one.. I can't believe I don't remember how to do any of this..Thanks.
http://oi44.tinypic.com/33dbec4.jpg
Hey guys, here's another one.. I can't believe I don't remember how to do any of this..Thanks.
http://oi44.tinypic.com/33dbec4.jpg
$\displaystyle f(x) = \frac{x}{x^2+2} $
determine $\displaystyle \frac{f(x+h)-f(x)}{h}$ in the simplest form
$\displaystyle f(x+h) = \frac{x+h}{(x+h)^2+2} $
and $\displaystyle f(x) = \frac{x}{x^2+2} $
so
$\displaystyle \frac{f(x+h)-f(x)}{h} = \dfrac{\dfrac{x+h}{(x+h)^2+2} - \dfrac{x}{x^2+2}}{h} $
try to cancel the h in the denominator
What happened to the denominators?
$\displaystyle \frac{\frac{x+h}{(x+h)^2+ 2}- \frac{x}{x^2+ 2}}{h}$
Get common denominators:
$\displaystyle \frac{(x+h)(x^2+2)}{h(x^2+2)((x+h)^2+ 2)}- \frac{x((x+h)^2+ 2)}{h(x^2+ 2)((x+h)^2+ 2)}$
$\displaystyle \frac{x^3+ hx^2+ 2x+ 2h- (x^3+ 2hx^2+ (h^2+2)x}{h(x^2+ 2)((x+h)^2+ 2)}$
Reduce the numerator. you can pretty much ignore the denominator. Once you cancel that original "h", the rest of the denominator goes to $\displaystyle (x^2+ 2)^2$.