Question

一道微积分题目。。。。

The high (in metres) of a model rocket t seconds after launching is given by
h(t)=3t^2
until the fuel runs out after 20s.

(1). find the average velocity of the rocket during each of the first four seconds.
(2). Find (in simplified form) the average velocity during an interval of time △t starting at t=2, t=6, and t=18.
(3). Using the results of part (2), , find the velocity at times t=2, t=6, and t=18

求过程。。。谢谢T T

Answer 1

1、(h(4)-h(0))/4=12(m/s)
2、t=2处，平均速度是(h(2+△t)-h(2))/△t=12+3△t。
t=4处，平均速度是(h(4+△t)-h(4))/△t=24+3△t。
t=6处，平均速度是(h(6+△t)-h(6))/△t=36+3△t。
3、t=2处的瞬时速度是lim(△t→0) (h(2+△t)-h(2))/△t=12
t=4处的瞬时速度是lim(△t→0) (h(4+△t)-h(4))/△t=24

t=6处的瞬时速度是lim(△t→0) (h(6+△t)-h(6))/△t=36

追问

= =第一个答案不对。。

然后后面是t=2,6,18