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)

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)
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

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)
----------------------- 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
-----------------------页面1 -----------------------
1 .（ 1 ）你能在图表的最大整数函数f （ x ） = [ x ]个
为X ∈ [ -3,3 ） 请继续这样做了下列问题：
（一）你能描述表达函数f （ x ） = [ x ]个为X ∈ [氮,氮离子1 ）
（ b ）是否在任何连续函数整数n
（ 2 ） ）请使用导数的定义显示
如果f是微在X和f （ x ）的“ 0 ,然后,
数/尖端（根号） √函数f （ x ） = f （ x ）的的导数/ （除以） 2 √ f （ x ）的
字母i
-----------------------页面2 -----------------------
2 .（ 1 ）计算给定的衍生物的职能.简化你的,
swers只要有可能.
（一）体积V =秒（十平方）谭（十平方）款（ b ）黄大仙（产地来源证（谭吨） ）
（ 2 ）寻找方程的线,是切线和正常的
曲线为y = （这是根号） √ 2产地来源证（十/ 4 ）在（ π ,1 ） .
（ 3 ）使用数学归纳法核实数/型x的ñ次方为N工作室的正1次方每
积极间北路
（ 4 ）使用交互规则得到的结果

页面一的问题太烦了，建议用Mathematica画图
页面二：(a) Sum(我这里代替积分号) Sum(sec^2x*tan^2x)dx=Sum(tan^2x)d(tanx)=1/3*tan^3x+C