Posted by Leanna on .
If the function f is defined by f(x)=x^22x, find limit h>0
(f(3+h)(f(3h))/2h

Calculus 
bobpursley,
first, f(3+h)=(3+h)^2 2(3+h)
= 9+6h+h^262h = h^2+4h+3= (h+3)(h+1)
second f(3h)=(3h)^2 2(3h)=
= 96h+h^26+2h=h^24h+3=(h3)(h1)
so first second then is
h^2h^2+4h+4h +33=8h
finally, lim 8h/2h=4
check all that. 
Calculus 
Leanna,
Thank you for your help!
For the second part I thought it would be (9+6hh^2)6+2h? 
Calculus 
bobpursley,
you put a minus sign in front of the first term? Why?

Calculus 
bobpursley,
and, the 6h term in (3h)^2=96h+h^2

Calculus 
Leanna,
(f(3+h)(f(3h))/2h
I put a minus sign because it has a negative in front of the f(3h) so it's (f(3h))