Question

美国高中数学。。

Answer 1

1.
f(x) = (2x+1)(x-5)/(3x(x+2)(x-1))
so, when x = -1/2, x = 5, funciton f(x) = 0,
the x-intercepts of f(x) are: -1/2, 5

when x->0, or x->-2, x->1, f(x)->∞， so the vertical asymptotes are the following lines:
x=0, x= -2, x= 1

when x->+∞ or x->-∞, f(x)->0, so the horizontal asymptote is:
y = 0

2.
a.
V = π r^2 h = 21.7
r = sqrt(21.7/πh)

b.
S =2πr^ + 2πrh
h = 21.7/πr^2
S = 2πr^2 + 2πr * 21.7/πr^2
S = 2πr^2 + 43.4/r

c.
S = (2πr^3 + 43.4)/r
when r->+∞, S->+∞, so S(r) has no horizonal asymptote

d.
S = 2πr^2 + V/r + V/r >= 3 (2πr^2 * V/r * V/r)^(1/3) = 3(2πv^2)^(1/3)
iff. 2πr^2 = V/r
r = (V/2π)^(1/3)
r = 1.51156 [inch]
meanwhile, h = 21.7/πr^2 = 3.023 [inch]

e.
omitted....

f.
maybe.... because it will looks like "square", be too urgly to be saled out? or, it is too wide to be easily held by one hand?

g.
no.
suppose we has a cylindrial container A has the same Height h with the prismatic container B.
when we keep they has the same Volume V, we can always find a r for A, to keep the same area of the up/bottom surface with B, but has a less perimeter than B, so that the total material surface area S(A) < S(B)

追问

确定吗？很重要正确