作业帮6道微积分数学题 国外大学的
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6道微积分数学题 国外大学的
6道微积分数学题 国外大学的
6道微积分数学题 国外大学的
dv/dt=a=F/m=-g
v=v0-gt
s=int v dt=v0t-.5gt^2
Assume the height of the cliff is h
then
(1) -h=v01t-.5gt^2
(2) -h=v02(t-1)-.5g(t-1)^2
(1)-(2) 0=48t-24(t-1)-16[t^2-(t-1)^2]
0=24t+24-16(2t-1)
8t=40
t=5
From(1)
h=16t^2-v01t=16*5^2-48*5=400-240=160 ft
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dv/dt=16
v(end)=0
v=v0-16t
t=v0/16
v0=16t
S=int vdt=v0t-8t^2=200
8t^2=200
t=5
v0=16*5=80ft/s
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The increase of the population from time t=0 to t=16
The population at t=16
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Since slope=derivative,so the integral means the increase of the height form x=3 to x=5
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f'(x)=df/dx=pounds/feet
int f(x)dx=pounds*feet
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The points are
pi/n,2pi/n,...,npi/n
The interval is (0,pi)
so h=(pi-0)/n=pi/n
The sum can be rewritten as
int sin(x)dx
=-cosx|
=2