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

For f(x)=x^2+x-2/x^2-4, determine the equation for any vertical asymptotes, the equation for any horizontal asymptotes, and the x-coordinates of any holes

csc beta = 2/3. What is the beta to the nearest degree?

Determine an example of a vector field that would yield a positive value for a line integral around a circle that is traversed once clockwise for any nonzero radius and explain how you know your vector field is correct.

Express the following systems of equations in matrix form as A x = b. What is the rank of A in each case (hint: You can find the rank of a matrix A by using rank = qr(A)$rank in R. For each problem, find the solution set for x using R.

a. X1+5X2+2X3=5

4X1-X2+3X3=-8

6X1-2X2+X3=0

b. 3X1-5X2+6X3+X4=7

4X1+2X3-3X4=5

X2-3X3+7X4=0

X2+3X4=5

. Let Π be a finite incidence geometry. Prove that, if every line in Π has exactly n points and every point in Π lies on exactly n + 1 lines, then Π is an affine plane. Come up with a similar criterion for finite geometries satisfying (EP) (those geometries are called projective planes).

why are the domain and range of square root function restricted to [0,∞) ?