For the function x^2+2x-4, find lim h--0 (f(h+4)-f(4))/h

Question

For the function x^2+2x-4, find lim h-->0 (f(h+4)-f(4))/h

lukecrayonz · Answer

lukecrayonz · Answer

another question after this.. you'll love it.. i think.

anonymous · Answer

$$f(4)=4^2+2\times 4-4=16+8-4=20$$
$$f(h+h)=(4+h)^2+2\times (4+h)-4$$
$$=16+8h+h^2+8+2h-4=20+10h+h^2$$
$$f(4+h)-f(4)=10h+h^2$$
$$\frac{f(h+h)-f(4)}{h}=\frac{10h+h^2}{h}=\frac{h(10+h)}{h}=10+h$$

anonymous · Answer

take the limit as h goes to zero, get 10

anonymous · Answer

in a week you will be able to do this problem in five second in your head (using a short cut)

lukecrayonz · Answer

Haha I hope, because honestly right now that looks just strange. Is that the ending answer?

lukecrayonz · Answer

Congratulations on 10,000 medals by the way.

anonymous · Answer

look carefully at all the steps. i left almost nothing out but a tiny bit of algebra
i know it looks long, but go through them carefully and see exactly 
1) what all the steps were
2) that in the numerator everything without an h disappeared (added to zero)
3) at the end you cancel the $h$ out of the denominator, so then you can take the limit by replacing $h$ by 0

lukecrayonz · Answer

http://screensnapr.com/v/N2Hpzu.png