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Graphs and Functions

Riemann Integrable Function : Upper and Lower Sums

Please see attachment. Q. Show directly that the function is integrable on R = [0,1] x [0,1] and find (Hint: Partition R into by squares and let N , limUp = limLp = integrable Up = upper Riemann sum of f respect to partition  U(f,p) = Lp = Lower Riemann sum of f respect to partition  L(f,p) =

Vector Components : Force


Examples of Functions : Exponentials, Graphs and Usefulness

1. Give an example of an exponential function. Convert this exponential function to a logarithmic function. Plot the graph of both the functions and post to the discussion forum. Discuss these functions and their graphs with your classmates. 2. Given the values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, x, and y, form each of the follow

Graph of polar equation

Inspect the four given graphs, which are plotted in polar coordinates (and shown in an attached .doc file), and choose the graph that corresponds to the polar equation r = 6 - (cos theta).

Chromatic Numbers

Use words to describe the solution process. No programming. 2. Let G = (V,E) be a graph where V {1,2,3,4,5,6,7,8,9,10,11,12} and E contains all edges connecting to vertices a and b such that ab=0 (mod 3). What is the chromatic number of G? Is G planar? See the attached file.

Complete the Graph Problem

Please use words to describe the solution process: Let G be a graph with n vertices that is not a complete graph. Prove that x (G) < n HINT: If G does not contain k3 as a subgraph, then every face must have degree at least 4. *(Please see attachment for proper symbols).

Graphs and Figures

Please use words to describe the solution process. Let G and H be the graphs in the following figure (see attachment): Please find x(G) and x(H). See the attachments.

Evaluate the Binomial Coefficient

Evaluate the combination or binomial function in the completion 48 factorial over 37 factorial. The answer should equal to 22595200368.

Lipschitz functions

A function f:A->R is called Lipschitz if there exists a bound M>0 such that Absolute value of f(x)-f(y)/x-y <=M for all x, y belong to A. Geometrically speaking a function f is Lipschitz if there is a uniform bound on the magnitude of the slopes of lines drawn through any two points on the graph of f. a- Show that if f:A->R i

Writing Equations Distributive Property

I must write an equation that has the solution x = -2 and graph it. My equation must include combining like terms on the left side and distributive property on the right side. I missed two weeks of class due to illness, and am having a hard time working this out. I just need a sample answer or starting point so that I underst

Graphical Representation of Linear Equation

Solve the following questions on graphical representation of linear equations. Your response should include the graphs for each of these questions. 1. Plot the graph of the equations 3x - 2y = -6 and 4x + 2y = -11 and interpret the result. 2. Plot the graph of the equations 3x - 5y = 14 and -6x + 10y = 9 and interpret

Divergence Criterion - Corollary

Corollary:(Divergence criterion for function limits).let f be a function defined on A, and let c be a limit piont of A. If there exist two sequences (x_n) and (y_n) in A with x_n not =c and y_n not =c and lim x_n=lim y_n=c but lim f(x_n) not = lim f(y_n), then we conclude that the functional limit lim f(x) as x->c does not exist

Differential Equations - Cross-Eyed Heart

27. y'' + 25y = sin(4t), y(0) = 0, y'(0) = 0. Plot the component curves and the orbit, the latter for the rectangle |y|< 0.25 and |y'|< 1. Any surprises? 28. Hearts and Eyes: Find a solution formula for y'' + 25y = sin&(wt), where w is not equal 5. Plot the solution curve of the IVP with y(0) = y'(0), where w=4. Plot t

Eulerian and Non-Eulerian Graphs

Let G be a connected graph that is not Eulerian. Prove that it is possible to add a single vertex to G together with some edges from this new vertex to some old vertices so that the new graph is Eulerian. Please see attachment for background and hints.

Graphs : Eulerian Trails

1. We noticed that a graph with more than two vertices of odd degree cannot have an Eulerian trail... (please see the attached file).

Graphs : Connectedness, Vertices and Edges

11. Let G be a graph with n>= 2 vertices. a) Prove that if G has at least (n-1) + 1 edges the G is connected. ( 2 ) b) Show that the result in (a) is best possible; that is, for each n>= 2, prove there is a graph with (n- 1)

Density function

A random variable X has the density function f(x)=...Find E(e^2x/3) Please see attached for full question.

Finding curves

Find the curve that passes through the points (3, 2) and has the property that if the tangent line is drawn at any point P on the curve, then the part of the tangent line that lies in the first quadrant is bisected at P.

Critical Point Functions

(-x^2/2(x+1)^3/2) + (2x/(x+1)^1/2)=0 , Critical points are any point in the domain or a function where the derivative is undefined or equals zero. The critical points are candidates for maximum and minimum values. To find the critical points set: =0

Computing 'Ambiguity' Equation

1. Calculate the ambiguity function of a signal with an envelope u(t) = Bexp(-t^2)T^2). What should be the value of B that will make the signal of the unit energy? 2. Calculate the ambiguity of a signal with a complex envelope u(t) = Bexp(-t^2/T^2)exp(jpikt^2). Note that this is the same signal as above, except for the additi