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# Graphs and Functions

### Determine the Laplace transform of the function.

Please see attachment Determine the Laplace transform of the function.

### Maximizing a Function given a Constraint

Maximize f(x,y) = sqrt(6- x^2 - y^2) given the constraint x+y-2=0.

### Calc

Find the Taylor polynomial of degree 4 of at c=4 and determine the accuracy of the polynomial at x=2.

### For the equation 4x-2y=6 find (a) slope (b) y-intercept.

For the equation 4x-2y=6 find (a) slope (b) y-intercept.

### How to graph the system of inequalities Y>2x-4, y<2x+1

Graph the system of inequalities and solve. Y > 2x - 4 y < 2x + 1

### Simple Function Operations

1a.)Is y=x^4 a single- or multi-valued function? b.)Is y=f(x)=x^2+4x an even, odd, or neither function? c.)What is the inverse function of y=x^4 d.)What is the inverse function of (b.),y=x^2+4x? e.)Is the inverse function from (d.), odd, even, or neither?

### Will Meteorites Travelling on a Parabolic Path Strike the Earth?

The earth with center at the origin has equation of xsquared + ysquared =65 where x and y are distances in thousands of kilometers. Will either of these two meteorites whose equations I will give you strike the earth? The first meteorite is a parabola whose equation is 18x-ysquared = -144. Please show all steps in sketching and

### Draw the Graphs for Three Equations and Find a Common Point

Using first two equations determine 3 possible points that the 2 conic sections that you get from equations meet. Add a third equation figure to out the one point that all three conic sections meet. First equation is 9(x-squared)+25(y-squared)-72x=81 Second equation is 9(x-squared)-15(y-squared)=9 Graph these two conical

### Green's Identity and Mean Value Theorem for Harmonic Functions

Please see the attached file for the fully formatted problems. Let h 2 C2(R3) be harmonic (h = 0). Using Green's identity for .... is independent of the value of R. Then one can deduce the mean value theorem .... Now what can you say if limx!1 h(x) = 0?

### Choosing Between Point-Slope, Slope-Intercept and Standard Forms

Find an example, of the BMI between man/woman and estimate a best fit line graphically. Develop an approximate linear model using the point slope form, the slope-intercept form or the standard form line. You are not to graph the line here but help illustrate your point . You are only required to use the line of the forms to iden

### Brouwer's Fixed Point Theorem

Please see the attached file for the fully formatted problems. Prove that if D is the closed disc |x| =< 1 in R2, then any map f E C2[D --> D] has a fixed point: f(x) = x. The proof is by contradiction, and uses Stokes theorem. Follow the steps outlined below. (1) Define a new map F(x) = ... ..... Show that F has no fixe

### Inverse Circular Functions for Acute Angles

Solve for: sin-1 (cos x) (Limit solution to an acute angle.)

### Spanning Tree Graph : Movie Collaboration (Kevin Bacon Game)

If you were required by a professor to find a spanning tree of the movie collaboration graph (where each node corresponds to an actor with finite Kevin Bacon number, and two nodes are connected by an edge if the corresponding actors have been in a movie together), how would you do it? Why would you choose your method over other

### Spanning Trees and Graphs

Does every graph have a spanning tree? If not, then can you tell from the number of nodes and the number of edges a graph has whether it has a spanning tree, or do you need more information?

### Functions, Inverse Functions and Graphs

1. Let h(x) = (8x - 5)/(7-x). (a) Find the inverse of the function h. Show work. (b) What is the domain of h? What is the domain of the inverse of h? 2. Use a calculator (standard scientific calculator or the online graphing calculator) to find each of the following values. Write your answer rounded to 4 decimal places.

### Moment generating function

The discrete rv W has the pmf pw(W) = klog[(w+1)/w] for w = 2,3,4,5; 0 otherwise k = 1/ log(3) (a) deduce the mgf of W (b) Calculate E[W] and var[W] using the mgf (c) Determine and sketch the distribution function of W

### Green's Function

Please see the attached file for the fully formatted problems. (a) FIND the Green's function for the operator with L = + w2 with u(a) = 0 dx2 u(b) = 0 and a < b, w2 a fixed constant. i.e. SOLVE Lu = ?ö(x ? ) with the given boundary conditions. (b) Does this Green's function exist for all values of w? If NO, what are the

### Area of a Region Bounded by Two Functions

Find the area of the region bounded by the graphs of y = x^2+3x&#8722;1 and 25x&#8722;3y = 19.

### Equation of a Tangent Line

Find the equation of the line tangent at the point (4,1). Given: sqrt(y) + x(y^2) =5

### Graphing Exponential Functions, Exponential Function Property

Can you please assist me withthe following problems. Please show the steps so that I can follow and gain a better understanding. Thank you for your assistance in this matter. Page 364-365 #6, 22, and 62 Page 371 Matched Problem 4 Page 373-375 #6, 12, 26, 44, 46, and 52.

### Find the slope and Y-intercept.

Find the slope and Y-intercept of: 1) -4Y=5X-6 2) 4X + 5Y = -20

### Straight Line and Slope

A) Explain what is the y-intercept and which letter represents it in the equation y = mx +b. b) If a and b are positive numbers, what is all the information we can deduce about the relationship between the lines: L1: y = - ax + b and L2: y = (1/a)x + b?

### Polar Function : Graphing an Ellipse

Graph an ellipse as a polar function with a focus at the pole and parameterized by the eccentricity e and the distance d between the focus and a vertical directrix. ----------------------------------------------------- Please show me how step-by-step on how you would graph this. Thanks

### Polar function

Graph an ellipse as a polar function with center at the pole and parameterized by the lengths of the semi-major and semi-minor axes. Can someone please show me step-by-step on how to do this?

### Functions: Radius of Convergence and Approximations

Please see the attached file for the fully formatted problems. Let f be the function defined by f(x) = sigma (starting at n=1 ending at infinity) xnnn /(3n n!) for all values of x for which the series converges. a) Find the radius of convergence of this series b) Use the first three terms of this series to approximat

### Dirac Delta Function

Please see the attached file for the fully formatted problem. Express d(xa) in terms of the Dirac delta "function" d(x), where a is a non-zero constant.

### Algebra : Graphing, Distance between Points and Equations of Lines

Please see the attached file for the fully formatted problems. Can you please help me with the following circled problems? Page 187 1. a) 12, b) 14, c) 16, d) 18 (Check for all four of our symmetries SY, SX, SO, SI; consult in WEEK7 NOTES, in COURSE CONTENT. Practice graphing these using the downloaded graphing utility Gr

### Reflecting a graph about y-axis

Explain about Reflecting a graph about y-axis and sketch the graph of g(x)=sqrt(-x)

### Reflecting a graph about the x-axis

Explain briefly about Reflecting a graph about the x-axis Sketch the graph of y=-x^2

### Vertical Shift Explanation

Explain about Vertical Shifting of Graphs Using this sketch the graphs of y=x^2+1 and y=x^2-2