Explore BrainMass

Graphs and Functions

Fixed Point : Mean Value Theorem

A number (a) is called a fixed point of a function (f) if f(a)=a. Prove that, if f'(x) does NOT equal 1 for all real numbers (x), then f has at most one fixed point.

Parallel Lines

Find the pair of parallel lines: 1: -y=-x+2 2: -2y-2x=2 3:-2x+2y=2 Not sure how to do the above problem.

Equations of Lines, Slopes, Intercepts and Word Problems

Please see the attached file for the fully formatted problems. 1. Find a linear function perpendicular to the function y= -5x + 12 at the point (2,5) in standard form, point slope form, and slope-intercept form. The orginal line is y = -5x + 12 (slope is -5), so the perpindicular line will be y = 1/5x + ? 5 = (1/5)2 + ?.

Functions : Domain, Intercepts, Symmetry, Asymptotes and Graphing

Given the function R(x) = X^2 + x -12 / X^2 - 4 1. Give the domain 2. Give the X - intercepts 3. Give the Y - intercepts 4. Does it have symmetry with respect to the Y-axis, the origin or neither? 5. Give the vertical asymptotes 6. Give the horizontal asymptotes 7. Graph the function by dividing the axis and te

What is the difference between functions and relations?

The question ask - in the real world, what might be a situation where it is preferable for the data to form a relation but not a function? Also, if the variables in an equation were reversed, what would happen to the graph of the equation? This was the example I was given, how would the graph of y = x² relate to the graph o

Estimating Roots by Newton's Method and Rate of Convergence

Please see the attached file for the fully formatted problem. 19. Show that x = tan^-1(x) has a solution alpha. Find an interval [a,b] containing alphasuch ythat for every x E [a,b] the iteration xn+1 = 1 + tan^-1(xn) n>=0 will converge to alpha. Calculate the first few iterates and estimate the rate of convergence.

Depreciation: linear functions, graphs, slope

Office equipment was purchased for $20,000 and is assumed to have a scrap value of $2,000 after 10 years. If its value is depreciated linearly (for tax purposes) from $20,000 to $2,000: (A) Find the linear equation that relates value (V) in dollars to time (t) in years. (B) What would be the value of the equipment after 6 yea

Simple interest: linear functions, graphs and slopes

The simple interest formula says that if $1,000 is invested at 7.5% (r=0.075), then A=75t+1000, t>=0. (A) What will $1,000 amount to after 5 years? After 20 years? (B) Sketch a graph of A=75t+1000 for t between 0 and 20. (C) Find the slope of the graph and interpret verbally.

Functions / Graphs : Domain, Range, Distance Between Points

1. Find the domain and range of the function: f(x)=6xsquared+4 2. Find the distance between the two plotted points;(-5,2) (4,-4) 3. Using graph of f(x)=x squared as a guide, graph the function; g(x)=(x-3)squared+4 _____________________________________________________________________ 2

Differential Equations - Cross-Eyed Heart

27. y'' + 25y = sin(4t), y(0) = 0, y'(0) = 0. Plot the component curves and the orbit, the latter for the rectangle |y|< 0.25 and |y'|< 1. Any surprises? 28. Hearts and Eyes: Find a solution formula for y'' + 25y = sin&(wt), where w is not equal 5. Plot the solution curve of the IVP with y(0) = y'(0), where w=4. Plot t

Computing 'Ambiguity' Equation

1. Calculate the ambiguity function of a signal with an envelope u(t) = Bexp(-t^2)T^2). What should be the value of B that will make the signal of the unit energy? 2. Calculate the ambiguity of a signal with a complex envelope u(t) = Bexp(-t^2/T^2)exp(jpikt^2). Note that this is the same signal as above, except for the additi

Approximation of Functions

Let f(x)=invertedCOS(x) for EQUATION1 (the principal branch of EQUATION2) Find the polynomial of degree two EQUATION3 which minimizes EQUATION4. *(Please see attachment for all equations)

Proof f(x)=x

Suppose that F is a continuous function on [0,1] and f(x) is in [0,1] for each x. Prove that f(x)=x for some x.

Trend Line Slope (Graph)

Please graph the attached trend line slope ALL I NEED TO GO WITH THIS IS A TREND LINE SLOPE THIS IS MY 3RD REQUEST. On March 1st the stock price was: $28.41 (Pi) On April 1st the stock price was: $28.91 (Pf) The slope is defined as: The trend predicts that the stock price will increase 0.5 dollars every month.

Vectors, graphs, and counting

Project 4A 1. Explain why vectors QR and RQ are not equivalent. 2. Explain in your own words when the elimination method for solving a system of equations is preferable to the substitution method. 1. In Washington DC, there is a large grassy area south of the White House known as the Ellipse. It is actually an ellipse wi

Word problems, graphs and equations, etc.

1 In a class, there are 20 men and 15 women. Find the ratio of the number of men to the number of students in the class. First express the ratio as a fraction reduced to lowest terms. Then re write the ratio using a second method. 2.Determine whether each of the ordered pair is a solution of 3x-4y>7: (0,0), (3,-6), (-


Which functions are one-to-one? Which functions are onto? Describe the inverse function A)F:Z^2-N where f is f(x,y) x^2 +2y^2 B)F:N->N where f is f(x) = x/2 (x even) x+1 (x odd) C)F:N->N where f is f(x) = x+1 (x even) x-1 (x odd) D)h:N^3 -> N where h(x,y,z) = x + y -z

Question about onto functions

Let P be the power set of {A, B} and let S be the set of all binary strings of length 2. A function f: P -> S is defined as follows: For A in P, f(A) has a 1 in the high-order bit position (left end of string) if and only if a is in A. f(A) has a 1 in the low-order bit position (right end of string) if and only if b is in A. Is


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