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Graphs and Functions

Sketch the region bounded by the graph of the function and find the area.

Sketch the region bounded by the graphs of the functions and find the area of the region. f(x) = sin(x), g(x) = cos(2x), -pi/2 <= x <= pi/6 (a) Use a graphing utility to graph the region bounded by the graphs of the equations, (b) find the area of the region and (c) use the integration capabilities of the graphing utility

Sketch regions bounded by graphs of algebraic functions and calculate the areas.

Sketch the region bounded by the graph of the algebraic function. 20. f(x) = -x^2 + 4x + 1, g(x) = x + 1 22. f(x) = -x^2 + 4x + 2, g(x) = x + 2 24. y = 1/(x^2), y = 0, x = 1, x = 5 26. f(x) = 1*sqrt(x - 1), g(x) = x - 1 28. f(x) = y(2 - y), g(y) = -y 30. f(y) = y/(sqrt(16 - y^2)), g(y) = 0, y = 3 32. g(x) = 4/(2 - x),

Slope Predictor Formula : Finding a Tangent Line to a Curve

1. Apply the slope-predictor formula to find the slope of the line tangent to y = f(x) = (2x+4)2 - (2x-4)2. Then write the equation of the line tangent to the graph of f at the point (3, f(3)). My attempt... I found y first by: f(x) = (2x+4)2 - (2x-4)2 f(x) = (4x2+16x+16) - (4x2-16x+16) f(x) = (4x2+16x+16) + (-4x2+

Square root equations

Solve the following equations and show your work: 1) sqrt of x - 2 = 1 2) sqrt of x^3 = 27 3) 3 sqrt of x^2 = 9 4) Is (sqrt of x)^2 an identity (true for all nonnegative values of x)? x -2 -1 0 1 2 y .111 .333 1 3 9 Given the table above, graph the function, identify the graph of the function (line, parabol

Graphing a Radical System of Equations

For the equation x- 2&#8730;x = 0, perform the following: Solve for all values of x that satisfies the equation. Graph the functions y = x and y= 2&#8730;x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.

Solving Linear Equations Word Problems

Section 3.1 # 94 Demand equation. Helen's Health Foods usually sells 400 cans of ProPac Muscle Punch per week when the price is $5.00 per can. After experimenting with the prices for some time. Helen has determined that the weekly demand can be found by using the equation D=600-40p, Where d is the number of cans and p is the

Solving and Graphing Linear Equations and Word Problems

Week 3 Discussion Questions-Linear Equations in 2 Variables 1. Paul and nine other students are taking a math class. He is worried about the content of the next quiz because he just can't solve those word problems. The teacher has said that the number of questions divided by the number of students = 2.8, and 14.3 % of the tes

Algebra Questions: IP unit 3

Algebra Questions. See attached file for full problem description. While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a ra

Y=x^2-6x+8 in to the form y=a(x-h)^2+k

Y=x^2-6x+8 in to the form y=a(x-h)^2+k How do you change the function? This initial problem is followed by: a) What is the equation for the line of symmetry for the graph of the function. (I think I can solve this ) Please explain and show in detail how to break this down in (dummy language) b) Asks that the functi

IP unit 1: Algebra Questions - Graphing, Domain, Range, Slope

1) a) Given the above graph, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function. Graph Type: Explantation: Domain: Range: b) Given the above graph, identify the gr

Fixed Point Iterations

1. The equation x - 3 ln x = 2 has exactly two solutions A and B, with 0 < A < B. (You do not have to show this.) (a) Show that A is in [0.5,0.7], and B is in [8.3,8.5]. (b) Consider the following fixed-point iteration for finding a solution of the given equation: xn+1 = e(1/3(Xn-2)): Show that if X0 = B+ E, where E is

Using a Graph to find the Maximum Area Enclosed; Volume Calculations

A rancher is building a rectangular corral and is using one wall of his barn as one of the sides. Because the barn wall is quite long, he needs fencing only along the other three He has 500 feet of fencing. The rancher wants the area of the conal to be as large as possible. should he choose as the dimensions of the corral? (Don'

Determine using Excel

Determine graphically using excel whether the equation could be possibly be an identity. If it can prove that it is. Here is an example of what I am working on at this time. Please explain how? cos 8x = cos^2 4x - sin^2 4x

Inverse function

Determine whether f (x)= (x-b)/a is one-to-one; if it is, find f^-1.

Parametric Equations

Find the parametric equations for the line through the point (1,0,-1) and parallel to the line (1/3)(x-4) = (1/2)y = z+2

Limits and Monotone Functions

First, I am looking for an example of a monotone function with (a,b)-->R that is unbounded and then I need to verify that the function has lim_x-->c^+ less than or equal to Lim_x-->d^- whenever a < c < d < b keywords: monotonic

Differentiable Functions : Lipschitz and Absolute Values

I have a function that is differentiable on [a,b] and I am trying to figure out which scenario is more restrictive: a) the function is a Lipschitz function with a Lipschitz constant L in (0,1) or b) the absolute value of f'(x) is less than one for all x in [a,b]

Proofs : Positive and Negative Functions

For a given function f, let f^+(x)=max{f(x), 0} and f^-(x)=max{-f(x), 0} Prove that for any function f, f=f^+ - f^- and |f|=f^+ + f^- Please see the attached file for the fully formatted problems.

Mean Value and Graphing

A) Sketch the Graph of y = cosx in the range -Pi < x < Pi. Hence Sketch the graph of y= |cosx| in the same range. (b) Find the mean Value of y= |cosx| in the range -Pi < x < Pi P.S its the |cosx| thats confusing me - I have never seen this format before.

Vertex, focus, directrix and latus rectum of Parabola and ellipse

1. Find the equation of a parabola whose vertex is (0,0) and directrix is the line y=3. 2. Find the vertex, focus, and directrix of (x-2)^2=12(y+1). Find the latus rectum and graph the parabola, making sure that all points and axis are labeled. 3. Find the equation of the ellipse whose center is the origin and has a