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Evaluating limits as h--->0?
Heres is a picture of my question
Lim (x+h)^3 - x^3/h
h--->0
How do I go about solving this? I know I'm supposed to plug in x+h wherever there is an h in the first f(x) but then I come out to
((x+h)+h)^3-x^3 divided by h and I have no idea what to do.
2 Answers
- notthejakeLv 79 years ago
(x + h)^3 = x^3 + 3x^2 h + 3 x h^2 + h^3
(x + h)^3 - x^3 = 3x^2 h + 3xh^2 + h^3 = h(3x^2 + 3xh + h^2)
[(x + h)^3 - x^3] / h = h(3x^2 + 3xh + h^2) / h = 3x^2 + 3xh + h^2
as h ==> 0, this goes to 3x^2
lim h ==> 0 is 3x^2
