(1) Find constants a and b that guarantee that the graph of the function defined by f(x)= will have a vertical asymptote at x = 5 and a horizontal asymptote at y = -3. (2) Find all vertical tangents and vertical cusps for each of the following functions. Justify your work. See attached file for full problem description.
What bound is given for X(G) by the theorem "for every graph G, X(G)<=1+max &(G') ,where the maximum is taken over all induced subgraphs G' of G" in the case that G is a) a tree? b) an outerplanar graph. Note: -&(G') this sign represent the minimum degree of G'. Yes it is that minimum -A graph G is outerplana
Prove for every graph G of order n, that n/B(G)<=X(G)<=n+1-B(G). X(G) is the minimum integer k for which a graph G is k-colorable is called the vertex chromatic number In the page 82 B(G) is defined like independent sets like you say but in the page 187 it other kind of B and it is define like Betti number and it is defi
Prove that a planar graph of order n>=3 and size m is maximal planar if and only if m=3n-6 What does maximal planar graph mean?
Prove : If G is a planar graph with n vertices, m edges and r regions , then n-m+r=1+k(G). K(G) is the number of component. Can you explain what is n-cube Qn and explain it step by step?
(8) Prove that Hom_Z(Z/nZ,Z/mZ) is isomorphic to Z/(n,m)Z
1. The x-coordinate of (-5,3) 2. The slope through the points (-2,5),(6,-3) 3. The y- intercept of 3x +7y =21 4. The slope of -10x-5y=0 5. The y-coordinate of (7,-6) 6. The x- intercept of -6x+6y=-6 7. Evaluate the function f(x)=3x-7forx=4 8. The slope through (8,6),(-4,0) 9. The y-intercept of y = 1/2x 10. The slop
1. The natural length of a spring is 10 cm. A force of 25 N stretches it to a length of 20cm. How much work, in units of N-cm, is done in stretching it from a length of 10cm to a length of 15cm? Hooke's law for a spring is given by f=kx, where f is the force, x is the distance the spring is stretched, and k is a constant. 2.
Graph each square root function and state its domain and range. y = (2 sqrt x) + 1
Graph each absolute value function and state its domain and range. See attached file for full problem description. y=|x-1| + 2
Determine whether the table expresses the second variable as a function of the first variable. c h 345 0.3 350 0.4 355 0.5 360 0.6 365 0.7 370 0.8 380 0.9
Find the value of arccos (-0.487) in radians.
Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, ratio
Determine whether the graph of the parabola opens upward or downward. See attached file for full problem description.
Let f(z) be holomorphic on |z|<1 and |f(z)|<1/(1-|z|) for |z|<1. Show that the Taylor coefficients an of f(z) satisfy:|an| less than ([(n+1)(1+1/n)]^n less than e(n+1)
Let f(z) be holomorphic in the region |z|<=R with power series expansion f(z)=sum(n=0 to infinity) a_nz^n. Let the partial sum of the series be defined as s_N(z)=sum(n=0 to N) a_nz^n Show that for |z|less than R we have s_n(z)= 1/i2pi(integral over |w|=R of f(w)[(w^N+1 - z^N+1)/(w-z)]dw/w^N+1).
If f(z) is holomorphic on |z|<1, f(0)=1, and for all |z|<=1 we have R(f(z))>=0, then show that -2<=R(f'(0))<=2 keywords: holomorphisms
What does a parabola open upward and when does it open downward? Please give an example.
Finding domain & range. See attached file for full problem description. (a) f(x) = (x -2)/ (3x + 4) (b) g(x) = -11/(4 +x) (c) g(x) = 4x^3 + 5x^2 -2x
7.1 Determine whether the correspondence is a function. 8. Domain Range Colorado State University University of Colorado ____________ > Colorado All three colleges points to college University of Denver Gonzaga University University of Washin
Graph and, if possible, determine the slope. Graph using the slope and the y -intercept. Determine whether the graphs of the given pair of lines are parallel. Determine whether the graphs of the given pair of lines are perpendicular. See attached file for full problem description. 7.4 Graph and, if possible, determi
Let G1 be a graph such that every two odd cycles intersect. Prove that X(G)=<5. (The minimum integer for which a graph is k-colorable is called the vertex chromatic number, or simply the chromatic number of , and is denote by , this problem is about graph coloring).
Please see the attached file for the fully formatted problems.
When crude oil flows from a well, water is frequently mixed with it in an emulsion. To remove the water the crude oil is piped to a device called a heater-treater, which is simply a large tank in which the oil is warmed and the water is allowed to settle out. Operating experience in a particular oil field indicates that the conc
Show that if two vertices u and v have the same score in a tournament T, then u and v belong to the same strong component of T. Can you explain what does score mean? Hint : Try to prove it on two lines. Definitely your proof shouldn't be longer than 4 lines! If it is longer, you are doing something wrong.
Graph the line with equation. See attached file for full problem description. Graph the line with equation . Can you please show the points on the line so I can see them. Thank you.:)
Please help me graph the line with equation: y=-5x-4 Also, show all of the steps so that I can learn how to do it myself.
Graph the line equation. See attached file for full problem description.
1. Plot the graph of the equations 2x - 3y = 6 and 2x + y = -10 and interpret the result. 2. Plot the graph of the equations 2x + 4y = 10 and 3x + 6y = 12 and interpret the result. 3. Determine graphically the vertices of the triangle, the equation of whose sides are given as y = x; y = 0; 2x + 3y = 10. Interpret the res
See attached file for full problem description. 1) Solve the following equations. a) Answer: Show work in this space. b) Answer: Show work in this space. c) Answer: Show work in this space. 2) Is an identity (true for all nonnegative values of x)? Answer: Expla