BOROUGH OF MANHATTAN COMMUNITY COLLEGE
City University of New York
Department of Mathematics
Mathematics Literacy Quantway I
MAT 041
Semester:
Credits: 0
Class hours: 4
Instructor Information:
Name:
Email:
Phone:
Course Description:
This developmental cou
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Place
Introduction phase
Growth phase
Own website
Alliance
Own shop/beauty salon
Franchise
We sell the product directly to end-users through our website and store.
We will using a Exclusive level of distribution intensity
Marketing Research Assignment
Zhuo Li
Mar100
March 25, 2017
Industry Research Paper
Traditional hair dyes and many shampoos contain harmful synthetic chemicals
that are routinely used on customers scalps and then washed down the drain where
they can accum
Zhuo Li
Marketing100
2/4/17
1. In this chapter we are briefly introduced to the marketing mix and the four Ps
product, place, promotion, and pricing. Can you identify examples of decisions
about each part of the mix that are being made in the cookie progr
Jiachen.Wang
Zhuo.Li
25/4/2017
Mar1001061
ProfessorShen
MPP3
part6
B. Exclusive will be the level of Distribution Intensity we are going to use for our
business. First of all, Eco-Friendly beauty hair salon is a very original hair salon product in
nowaday
Student Survey
Important!
Please paste your photo below:
Name: Zhuo Li
Email: zhuokangli@gmail.com
Mobile: 9178733328
Semester: 5
Major: Engineering
1. What courses have you completed?
ACC 122, AFN 121, CHE 201, CHE 202 ,MAT 161, MAT 206, MAT 301, SCI 120
Borough of Manhattan Community College
Department of Mathematics
MAT 008 Final Examination Practice
Form A
The actual final exam will have 24 questions: 20 multiple choices (4 points each) and 4 short
answers (5 points each). Please do not assume that the
HW1.4: Series, integral test - solutions
Apply the integral test to the following series and state your conclusion about convergence.
1. n=0 n en
the integral converges, so the series converges
2.
2
+2
n=0 n 33n
+2n+2
the integral diverges, so the series
HW 6.3 Chain Rule & Implicit Differentiation - solutions
dz
a) as a general formula b) at the given t-value
dt
1. z = x3y2 x = cos t & y = sin t t = /3
x(/3)=.5, y(/3)=3/2
dz
= 3x2y2(-sin t)+2x3y(cos t) OR -3cos2t sin3t + 2cos4t sint
dt
dz 7 3
at t = /3,
HW 6.6 Optimization with a constraint using Lagrange multipliers - solutions
1 Optimize f(x,y) = x2-y2 with the constraint 2y-x2=0
2 Optimize f(x,y) =6-x2-y2 with the constraint x+y-2=0
3 Find the greatest and least distance between the point (2,1,-2) and
HW 6.2 The tangent plane & differentials
For each function, find (a) the equation of the tangent plane, written in two notations: z-z0 & L(x,y) (b)
the formula for dz (d) the approximation for the function value at the nearby point using the linear
formul
HW 6.5 Maximum & minimum
Find the extrema of the function and classify them using the second (partial) derivative test
1 f(x,y) = -x3+4xy-2y2+1
2 f(x,y) = x2+y2+x2y+4 also find the absolute max & min on the region defined by -1x1, -1y1
3 find the dimensio
HW 1.10: Power Series - solutions
For what values of x does each series converge? Give the (a) interval (b) center (c) radius
1.
n=1 (1)n
n2 x n
2n
n2 2 n
check endpoints: x = 2: n=1 (1)
=
(1)n n 2 by n-th term test, diverges
n
n=1
2
2
n
n n (2)
=n=1 (1)n
HW 7.1 - Double Integrals & Volume - solutions
Calculate the iterated integral
4
2
3
5
1.
1 0 6 x 2 y2 x dy dx
2.
1 1
ln y
dy dx
xy
Calculate the volume for the surface f(x,y) for the given region R
x y2
3. f(x,y) = 2
R: 0<x<1, -3<y<3
x +1
4. f(x,y) = xy2
HW 5.1 Surfaces, Functions, Level curves
Match the function & graph & contour map [please write your answer in the form 6FVI]
1) z=sin(xy)
2) z=sin(x-y)
3) z=(1-x2)(1-y2)
4) z=excos(y)
5) z=sin(x)-sin(y)
6)
z=
7) One contour map is for a cone, the other i
HW 1.6: Series, limit comparison test - solutions
Apply the LCT (possibly in combination with other tests) and state your conclusion about convergence.
1.
1
n=2
n n21
1/n2 converges so this series converges
by LCT:
2.
n
n=2 n+1
1/n1/2 diverges so this ser
1.11 Power Series as Functions - solutions
Use the fact that
for |x|<1 to find the power series for
the following functions
1
1. h(x) =
1+x
S = n=0 (1)n x n = 1 x + x2 x3 + x4 - .
2. p(x) = ln(1+x)
x n +1
x2 x3 x4
by integration, S = C+n =0 (1)n
=C+x + +.
HW 9.2: Line integrals (for scalar functions or vector functions) solutions
1. Find the area under the function f(x,y)=y3 over the curve C defined by r=(t3,t) for 0<t<2
2. Find the area under the function f(x,y,z)=xyez over the curve C defined by r=(3t2,t
Name_
Surface Color_
The Hot Plate
Given a graph in 2-dimensions of y=f(x) but no formula, to get the slope at a point, we need to measure
x and y. To do this, we can put a ruler as the tangent line flat on the paper, make a right triangle, then
measure x
HW 1.5: Series, the direct comparison test
Apply the direct comparison test (possibly combined with other tests) and state your conclusion about
convergence.
1/ n
1.
n=1 en 2
2.
n=0 3n42
3.
n=0 2n3
n
1
arctan n
n1.2
k sin k
5. * k =0
3
1+k
3
6. n=0 2
n +1
HW1.4: Series, integral test
Apply the integral test to the following series and state your conclusion about convergence.
1. n=0 n en
2
2.
+2
n=0 n 33n
+2n+2
3.
n=1 en 2
4.
n=3 n (ln n)2
5.
n=0 n+3
6.
n=0 n 2+1
1/ n
1
1
3
7. why does the integral test wor
HW 3.4 Vector Cross Product - solutions
1. Find a vector perpendicular to (4,-3)
(3,4) or a multiple
2. Find the area of the parallelogram with sides (3,-1,5) & (2,5,-2)
3
2
23
1 X 5 = 16
5
2
17
( ) ( )( )
area =
232+16 2+172= 107432.77
3. Find both the
HW 3.2 vectors - solutions
1 find the vector which starts at (3,4) and ends at (5,1). also find its length
v = (2,-3), |v| = 13
2 find the vector which starts at (4,-2,3) and ends at (-3,5,1). also find its length.
v = (-7,7,-2) |v| = 102
u = (2,1) and
v
HW 1.9: Series, root test
Apply the root test (possibly in combination with other tests) and state your conclusion about
convergence.
1.
2.
3.
n=1
n=1
n=1
n
( )
( 1+nn )
( 2n+3
4n2 )
n
1+n
n
2
n
4. Why does the root test work well on the above series?
HW 1.8: Series, ratio test
Apply the ratio test (possibly in combination with other tests) and state your conclusion about
convergence.
1.
n!
n=1 n n
so the series converges
1
2. n=0
n!
so the series converges
2n
3. n=0
n!
2
so the series diverges
n
10
4.