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Graphs and Functions

Differentiability, Bounded Above and Supremums

1. Let A and B be two nonempty sets of real numbers. Define A+B = {a+b: a belongs to A and b belongs to B}. (a) Show that if A is open, then A+B is open. (b) If A and B are both closed, is A+B closed? Justify your answer. 2. Let f be differentiable for x > a and A as x --> infinity. Prove that there is a sequence x_n --> infi

Graph and simultaneous equations

Accurately and neatly graph and label each of the equations and estimate the point of intersection of the two lines. Mathematically solve for the exact point of intersection of your two lines compare your mathematical solution with your graphical solution. Similar? Why? Not similar? Why or why not x + 2y = 14 4x - 2y = 18

Length of Polygonal Line Segments and Length of a Curve and Distance Formula

Find the total length of the polygonal line segments joining the points (xi, f(xi),i=0, 1,...,n, zwhere a= x0,x1,... xn=b is a regular partition of (a,b). use the indicated values for n (1) f(x) = sqrt x, a=0,b=4 (a) n=2, (b) n=4 (2) f(x) = sin^2 x, a=0, b= 2pi (a) n=2 (b) n=4 (c) n=8 (3) Use a y integration to find

Solve the following linear program using the graphical solution

(See attached file for full problem description with proper equations and diagrams) --- Graphical solution procedure Please help solve this linear problem in the attachment using the graphical solution procedure & graph the feasible region: Solve the following linear program using the graphical solution procedure: M

Directed Graphs, Vertices and Distinct Paths : Recall that R^3={(x,y,z):x,y,z(subset of R)}. Let G(V,E) be a directed graph, in which V= {(x,y,z)-(subset of R^3) :x,y,z(subset of R),-10<=x,y,z<=10}...

6. Recall that R^3={(x,y,z):x,y,z(subset of R)}. Let G(V,E) be a directed graph, in which V= {(x,y,z)-(subset of R^3) :x,y,z(subset of R),-10<=x,y,z<=10}. Suppose that for any vertex, v=(x,y,z)--[subset of V], the only edges originating at v are the ones joining v to (x+1,y,z),(x,y+1,z),(x,y,z+1) . i.e. any path that originate

What are all the intercepts of the graph of...? (6 Problems)

20. At what points does the graph of y = x^2 - 3x -10 cross the x-axis 21. What are all of the intercepts of the graph of y = 15x^2 + 89x - 6? 22. What are all the intercepts of the graph of y = 2x^2 - 11x + 5? 23. What are all the intercepts of the graph of y = 6x^2 + 13x + 6? 24. What are all the

Tarea de clase

(See attached file for full problem description with equations) --- 1.- Let , . Does is uniformly converge on (-1,1)? --- We use the book Methods of Real Analysis by Richard Goldberg.

Functions

Please show details of how to arrive at the solutions so I can understand how to do similar problems. (See attached file for full problem description with equations) --- (1) Given that the polynomial function has the given zero, find the other zeros. (2) Find the horizontal asymptote, if any, of the rational function.

Functions And Notation

1. From the function f (x)=IxI How would I go about finding its image set using interval notation? 2. Again using interval notation, how would I go about finding the image set of the graph g(x)= Ix+3I -2 ? And how then would I go on to solve the equation g(x)=1, and discover if it had any geometrical significance? 3. How

Lines and Circles

Say I have for example a circle with centre C(7,-5) passing through point A(6,-3) (With tangent line and radius, AC, being perpendicular.) 1. How would I go about finding the gradient of the tangent? 2. How would I go about finding that the equation of the tangent at A is the line x=2y+12 ? 3. And how would I go about find

Root

(See attached file for full problem description with equation) --- Solve this problem. Explain why has a root, and indicate an interval where this root lies. ---

Differentiation

Please sketch a graph of an arbitrary function f that satisfies the given condition but does not satisfy the conditions of the Mean Value Theorem on the interval [-5,5] f is not continuous on [-5,5]. Please offer as much explanation as practicable.

Graphing

Graph f(x) = 5x^2 / (x^2) + 2 I need to know the x and y intercepts and all known asymptotes

Find maximum subject to constraint and use result in proof

(See attached file for full problem description with equations) --- Find the maximum value of the function subject to the constraint . Use the result to prove that Use a similar method to prove that for any positive numbers ,... ---