Question

evaluate limit:

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

Answer 1

is that x+h or 3+h?

Answer 2

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

Answer 3

\[(x+h)^3=x^3+3x^2h+3xh^2+h^3\]

Answer 4

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

Answer 5

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

Answer 6

yes thats it. sorry if i was confusing

Answer 7

how did i guess?

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

i will find it