evaluate limit:

lim ((x+h)^3 -3)/h
h-0

Question

evaluate limit:

lim       ((x+h)^3 -3)/h
h->0

anonymous · Answer

is that x+h or 3+h?

anonymous · Answer

it is the quantity (x+h) to the third power minus 3. all over h

anonymous · Answer

$$(x+h)^3=x^3+3x^2h+3xh^2+h^3$$

anonymous · Answer

there is no limit because you get 
$$\frac{x^3+3x^2h+3xh^2+h^3-3}{h}$$
nothing factors, nothing cancels. which is why i am wondering if there is a typo because it looks like you are trying to find a derivative, but something is amiss

anonymous · Answer

are you sure it isn't 
$$\lim_{h\rightarrow 0}\frac{(x+h)^3-x^3}{h}$$

anonymous · Answer

yes thats it. sorry if i was confusing

anonymous · Answer

how did  i guess?

anonymous · Answer

$$\frac{(x+h)^3-x^3}{h}=\frac{x^3+3x^2h+3xh^2+h^2-x^3}{h}=\frac{3x^2h+3xh^2+h^3}{h}$$
$$=\frac{h(3x^2+3xh+h^2}{h}=3x^2+3xh+h^2$$

anonymous · Answer

take the limit as h goes to zero get 
$$3x^2$$ and in a week you will be able to do this instantly in your head

anonymous · Answer

wow thank you, could you help me on the other problem i posted??

anonymous · Answer

i will find it