# Math Help - Limits

1. ## Limits

Im struggling with this problem. lim h approaching 0 f(x+h)-f(x)/h for f(x)=4x^2-x
if anyone could help me that would be great

2. Originally Posted by mxhockey140
Im struggling with this problem. lim h approaching 0 f(x+h)-f(x)/h for f(x)=4x^2-x
if anyone could help me that would be great
$f(x) = 4x^2-x$

$f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

$= \lim_{h \to 0} \frac{4(x+h)^2-(x+h) - 4x^2+x}{h}$

$= \lim_{h \to 0} \frac{4x^2+8xh+4h^2-x-h - 4x^2+x}{h}$

$= \lim_{h \to 0} \frac{8xh+4h^2-h}{h}$

Take out a factor of h on the top and bottom, and you should get a result you can work with.

$= \lim_{h \to 0} 8x+4h-1$

3. thank you!