### Fixed point of a compressing function on metric space

Fixed point of a compressing function on metric space See attached file for full problem description with symbols.

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Fixed point of a compressing function on metric space See attached file for full problem description with symbols.

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.

1. For medical purposes the level of sugar was measured in blood (in mg/dl). The samples were taken with 1 2hr increments, as the following table shows: initial sample 96 mg/dl after 30 min. 133 mg/dl after 60 min. 142 mg/dl after 90 min. 81 mg/dl after 120 min. 87 mg/dl Graph in MATLAB sugar curves corresponding to thes

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.

Find any critical numbers of the function. h(x) = sin^2x + cosx 0 is less than x which is less than 2pi

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

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

(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 ,... ---

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.

If X is a connected space containing more than one point, and if {x} is closed subset for every x is a member of X show that the number of points in X is infinite.

Find equations for the tangent plane and normal line of f(x,y)=6-3x2-y2 at the point P(1,2,-1). ---

1. F(x) = -2cosθ 2. f(x)= -tanθ - 2 3. f(x) = (θ + pi/4)

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.

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

Let f: R --> R be the function defined by f(x) = x2 + 3x - 4 for all x E R. a) Determine wheter or not f is injective. b) Determine wheter or not f is surjective. c) Find f^-1({0,75/4}). d) Find f([0,1]).

1. If U.S. Treasury yields are as follows: 3 month 6.0% 6 month 6.3% 1 year 6.5% 2 year 6.6% 5 year 6.4% 10 year 7.5% 30 year 8.0% a. What is the expected yield on notes from year 1 to 2, assuming the PEH holds? b. What is the expected yield on notes from year 2 to 5, assuming th

(See attached file for full problem description with equations and diagrams) --- 1. Simplification of linear algebraic expressions and expressions with fractional coefficients and solve x; 2. Solving simple linear equations with fractional coefficient: 3. Solving inequalities with fractional coefficient: 4.

F(x) = 4sinx / (2sinx+4cosx) the equation of the tangent line to f(x) at a=0 is y=sx+b Find: y=sx+b

The parabola y= x^2+4 has two tangents which pass through the point (0,-2). One is tangent to the parabola at (a, a^2+4) and the other at (-a, a^2+4) where a is a certain positive number. The question is a=?

F injective iff there exists g such that gf = 1 f surjective iff there exists h such that hf = 1.

Please explain how to sketch a graph of a differentiable function f such that f > 0 and f' < 0 for all real numbers x.

Please explain how to find a and b such that f(x) = {a(x^3), x is less than or equal to 2 {x^2 + b, x is greater than 2 is differentiable everywhere

Y=3x^4+4x^3-6x^2-12x What are the points where tangent line is horizontal? What is the relative maxima and minima? Intervals of decrease? Points of inflection? and interval(s) of concavity?

See attached file for full problem description with equation. --- Find analytically the solution of this difference equation with the given initial values: Without computing the solution recursively, predict whether such a computation would be stable. (Note: A numerical process is unstable if small errors made at one

If x<-4, f(x) = {[-2(x^3) - 6(x^2) +14x+24] / (x+4)} if x>=-4, f(x) = 5(x^2) +5x+a What value must be chosen for a in order to make this function continuous at -4? Please note the value of a does not equal to 66.

Evaluate the sum (using generating functions) A) 0+3+12+...+3n2. B) 4x3x2x1+5x4x3x2+...+n(n-1)(n-2)(n-3)

(a) Suppose the graph in Figure 4.1.78 is that of a function g(x). Sketch the graph of the derivative g; (b) On the other hand, suppose the graph above is that of the derivative of a function f. For the interval ..., tell where the function f is (i) increasing; (ii) decreasing. (iii) Tell whether f has any extrema, and if so

For the function of f, given below in graph (a) Sketch (b) Where does change its sign (c) Where does have local minima and maxima Using the graph of write a brief description of complete sentences to describe the relationship between the following features of the function of: (a) the local maxima and minima o

Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). y = -x2 + 3x - 3 Here, a = -1, b = 3, c = -3 The axis of symmetry is x = -b/2a = -3 (-2) = 1.5 See attached file for full problem description, equations, charts and diagrams.

Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). y = -x2 + 3x - 3