问题描述：
英文高数微积分题求解（答得好追加100）
----------------------- 页面 1-----------------------
1.(1) Can you give the graph of the Greatest Integer Function f (x) = [x]
for x ∈ [-3,3)?Please continue to do the following questions:
(a) Can you describe the expression of f (x) =[x] for x ∈ [n,n + 1)?
(b) Is function continuous at any integer
(2) )Please use Definition of Derivative to show
if f is differentiable at x and f (x) > 0,then,
d/dx （根号）√f(x)= f(x)的导数/(除以）2√f(x)
i
----------------------- 页面 2-----------------------
2.(1)Calculate the derivatives of the given functions.Simplify your an-
swers whenever possible.
(a)v = sec(x平方 ) tan(x平方 ) (b) sin(cos(tan t))
(2) Find equations for the lines that are tangent and normal to the
curve y = （这是根号）√2 cos(x/4) at (π,1).
(3)Use Mathematical Induction to verify that d/dx x的n次方 = n*x的n-1次方 for every
positive inter n.
(4)Use the Reciprocal Rule to get the result for negative integer n.
ii
----------------------- 页面 3-----------------------
3.(1)How fast is area A of a circle increasing with respect to its radius
when the radius is 6cm?
(2) The cost of manufacturing x refrigerators is ￡ C(x),where
C(x) = 8,000 + 400x - 0.5x的平方
(a) Find the marginal cost if 100 refrigerators are manufactured.
(b) Show that the marginal cost is approximately the di?erence in cost
of manufacturing 101 refrigerators instead of 100.
iii
----------------------- 页面 1-----------------------
1.(1) Can you give the graph of the Greatest Integer Function f (x) = [x]
for x ∈ [-3,3)?Please continue to do the following questions:
(a) Can you describe the expression of f (x) =[x] for x ∈ [n,n + 1)?
(b) Is function continuous at any integer
(2) )Please use Definition of Derivative to show
if f is differentiable at x and f (x) > 0,then,
d/dx （根号）√f(x)= f(x)的导数/(除以）2√f(x)
i
----------------------- 页面 2-----------------------
2.(1)Calculate the derivatives of the given functions.Simplify your an-
swers whenever possible.
(a)v = sec(x平方 ) tan(x平方 ) (b) sin(cos(tan t))
(2) Find equations for the lines that are tangent and normal to the
curve y = （这是根号）√2 cos(x/4) at (π,1).
(3)Use Mathematical Induction to verify that d/dx x的n次方 = n*x的n-1次方 for every
positive inter n.
(4)Use the Reciprocal Rule to get the result for negative integer n.
ii
----------------------- 页面 3-----------------------
3.(1)How fast is area A of a circle increasing with respect to its radius
when the radius is 6cm?
(2) The cost of manufacturing x refrigerators is ￡ C(x),where
C(x) = 8,000 + 400x - 0.5x的平方
(a) Find the marginal cost if 100 refrigerators are manufactured.
(b) Show that the marginal cost is approximately the di?erence in cost
of manufacturing 101 refrigerators instead of 100.
iii
问题解答：
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