y''+4y'+4y=2e^{-2x} Find general solution.

The population of Egypt in 2002 was 73,312,600 and was 78,887,000 in 2006. Assume the population of Egypt grew exponentially over this period.

1.   Determine the 4-year growth factor and percent change.

2. Determine the 1-year growth factor and percent change.

3. Define a function that gives the population of Egypt in terms of the number of years that have elapsed since 2002.

4. Re-write your function from part(c) so that it gives the population of Egypt in terms of the number of decades that have elapsed since 20002.

5. Assuming Egypt’s population continued to grow according to this model, how long will it take for the population of Egypt to double?

We got for x > 0 given a differential equation y’ = 1-y/x, with start value y(2)= 2

1. Find the Taylor polynomial of first and second degree for y(x) at x =2.
2. Show that y(x) =x/2 +2/x solves the given equation.

For the function

a) f(x)=x^3-9x^2+23x-15

b)f(x)=(x+3)^2(2x+1)(x-1)

c)f(x)=-(x^2-6x+9)(x^2-x-6)

Find:

1) the zeros

2) the y-intercept

3) left-right end behavior

4) the sketch of the graph

T/F and why(true/false)?

(Part a) If the partial derivatives f_x(x,y), f_y(x,y) exists for all values x,y ,then f(x,y) is continuous.

(Part b) Suppose f(x,y) is a function which is differentiable and nonnegative everywhere, and is zero at the origin

,f(x,y) ≥ 0, f(0,0) = 0.Then the gradient vector is zero at the origin is,∇f(0,0) = (0,0).

(Part c) If F(x,y) is continuous on the entire plane, then there is a function f:R→R satisfying

f′(x) =F(x,f(x)), f(0) = 0 for all x∈R.

solve using series solutions

(x^+1)y''+xy'-y=0

Consider a solid object with the base in the first quadrant bounded by y(x) = 1-( x^2/16) , x-axis, and y-axis. If the cross section that perpendicular to the x-axis is in the form of square, determine the volume of this object!

A computer aided drafting (CAD) instructor at a community college wants to use his rapid prototype machine to produce demo items for a seminar on engineering technology. He plans to bring two different types, a Golden Ruler and a Fibonacci Gauge. He will bring at least 20 of each. he has 45 cubic inches of filler and 95 cubic inches of material available to make the demos, but only has 86 hours of free time to run the machine. he is able to save time by running the demos in batches. Use the information in the table to determine how many of each demo item he needs to bring while minimizing the total cost. Set up but do not solve.

What can you say about the following three sequences?

1 ) sequence = range [0, 100, 7]

{0, 7 ,14 ,21 ,28 ,35 ,42 ,49 ,56 ,63 ,70 ,77 ,84 ,91 ,98]

2 ) sequence = range [7, 100, 7]

{7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98}

3 ) sequence = table [ x^2, {x, 0, 17} ]

{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289}

___________________________________________________________

A. All three sequences are arithmetic sequences.

B. Only two of the three sequences are arithmetic sequences.

C. All three sequences are geometric sequences.

D. Only two of the three sequences are geometric sequences.

Theorems need to know a) The fundamental Thm of Algebra. b) The Rational Zero Thm. c) The intermediate Value Thm. d) The Conjugate Thm.

Evaluate the line integral

F · dr,

where C is given by the vector function r(t).

F(x, y, z) = sin(x) i + cos(y) j + xz k

r(t) = t⁵ i − t⁴ j + t k, 0 ≤ t ≤ 1

find the general solution to the second order linear non-homogeneous differential equation
(y"/2)-y' +y = cos x

Given: f(x) = x 2−36 x 2−7x+6 Find the following

a. V.A.

b. Domain

c. H.A.

d. X-intercept

e. Y-intercept

f. Graph

Find the tangential and normal components of the acceleration vector. ? (?) = ? ? ?̂+ √2 ? ?̂+ ? −??̂

-Let O (0,0,0) be the origin and A(a+1,b,c) where a,b and c are the last three digits of your student ID. Find, describe and sketch the set of points P such that OP is perpendicular to AP

- Let u=<a , b+1 , c+1> find and describe all vectors v such that |u x v|=|u|

a=1 , b=1 , c=9