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    Graphs and Functions

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    Tarea De Clase Uniform Converges

    (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.

    Uniform Convergence & Pointwise Convergence

    Let {fn(x)} n-1 ---> infinity be a sequence of continuous functions [0,1] that converges uniformly. a) Show that there exists M>0 such that |fn(x)|<= M (nЄI 0<x<1) b) Does the result in part (a) hold if uniform convergence is replaced by pointwise convergence?

    Asymptotes and zeros 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 interval 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

    Gradient and equation of tangent

    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

    Drawing Graph with Asymptotes

    Please explain how to create a function whose graph has the indicated characteristics for each of a and b (a) Vertical asymptote: x = 5 Horizontal Asymptote: y = 0 (b) Vertical asymptote: x = 5 slant asymptote: y = 3x +2

    Roots of functions

    (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. ---

    Quadratic Function : Graphing and Maximizing Profit

    The total profit, p(x) in dollars for a company to manufacture and sell x items per week is given by the function p(x)=-x^2+50x - Graph the function and label the x and y-intercepts on a scale where y-axis ranges from -100 to 900 and x-axis ranges from 0 to 55 - What is the maximum profit earned by the company in a week?

    How do you prove on the basis of the definition, the function

    My definition goes: If the function has its derivatives at point (a,b) then the function is differentible at (a,b) How do you prove on the basis of the definition, the function f defined by f(x,y)=xy(x+y) is differentiable at every point of its domain?

    Properties of Continuous Functions : Intermediate Value Theorem

    Suppose that functions f,g : [a,b] -> R are continuous, satisfy f(a) <= g(a) and f(b) >= g(b). Then there exists a real number c in [a,b] such that f(c) = g(c). Label the statement as true or false. If it is true, prove it. If not, give an example of why it is false and if possible, correct it to make it true.

    Undirected Graph, Spanning Tree, Joining Nodes and Ancestors

    Let G be an undirected graph, and let T be the spanning tree genereted by a depth-first search of G. Prove that an edge of G that has no corresponding edge in T cannot join nodes in differect branches of the tree, but must necessarily join some node v to one of its ancestors in T.

    Graph of an arbitrary function f that satisfies the conditions

    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 and Asymptotes

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

    Closest point to a function

    Let F(x) = x^.5 find the point on the graph that is closest to the point (4,0) write the complete ordered pair.

    Maximum Value of Subject to Constraint

    (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 ,... ---

    Determine the Function Inverse

    1. If f(x) = 4x2 - 12x + 9 for x ≥ 0, what is f-1(9)? Please see the attached file for the fully formatted problems.

    Slope

    What is the slope of the line passing through the two points (2,3) (0,6)?

    Horizontal tangent lines

    The graph of f(x) = 2x^3+9x^2-108x+14 has two horizontal tangent lines. Find the two values of x where the tangents occur.

    Zeros, Roots, Asymptotes, Domain of Intercepts, and Functions

    1. If Q(x) = -P(x), do P(x) and Q(x) have the same zeros? Why or why not 2. graph f(x) = + 5x+ 4 be sure to label all the asymptotes and to list the domain the x and y- intercept 3. f(x) = +3, x a. sketch the graph and use the graph to determine whether the function is on