Question
evaluate the limit
as lim h goes to 0
((2+h)^3 - 8)/h
the answer is twelve but I don't know how to factor out the cube
as lim h goes to 0
((2+h)^3 - 8)/h
the answer is twelve but I don't know how to factor out the cube
Answers
bobpursley
expand the (2+h) term
(2+h)(4+4h+h^2)
8+8h+2h^2+4h+4h^2+h^3
then, in the numerator, subtract 8 so the result is
12h+6h^2+h^3
divided by the denominator h
12+6h+h^2 and the limit as h>>zero is 12
(2+h)(4+4h+h^2)
8+8h+2h^2+4h+4h^2+h^3
then, in the numerator, subtract 8 so the result is
12h+6h^2+h^3
divided by the denominator h
12+6h+h^2 and the limit as h>>zero is 12