Let f and g be the functions given by f(x) = ¼ + sin(Pi*x) and g(x) = 4^ -x. Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of f and g, and let S be the shaded region in the first quadrant enclosed by the graphs of f and g. a) Find the area of R. b) Find the areas of S. c) Find t
Using maple 10: Given the curve: f(x,y)=12+10y-2x^2-8xy-y^4 a. Find the critical points correct to 3 decimal places b. Classify the critical Points cf. Generate and graph; identify the highest point on the graph
Using maple 10 do the following: a. Using a graph(s) estimate the local max., min., and saddlepoints of f(x,y)=x^3-3x+y^4-2y^2 b. Again using Maple use calculus to find these values exactly
(See attached file for full problem description)
Please explain in as much detail as possible finding an equation in standard form for each conic. 1) Parabola, focus (-4,0), directrix X=2 2) Hyperbola, foci (0, +/_3), vertices (0,+/-1) 3) Ellipse, center (2,2), a focus (0,2), vertex (5,2)
(See attached file for full problem description) --- 10. y = √x + 3 (√x+3 is all squared). Please use the Chain Rule 16. f (w) = w √w + w² (√w is only squared) Please use the Chain Rule 18. y = 4x³ - 8x² Please use the Chain Rule
Water is pumped_into an underground tank at a constant rate of 8 gallons per minute. Water leaks out of the tank at the rate of √(t+1) gallons per minute for 0 ≤ r ≤ 120 minutes. At time t = 0, the tank contains 30 gallons water. (a) How many gallons of water leak out of the tank from time r = 0 to r = 3 minut
4. Let h(x) be a function deflned for all ... such that h(4) = ?3 and the derivative of h(x) is given by .... (a) Find all values of x for which the graph of Ii has a horizontal tangent, arid determine whether 1 has a local maximum, a local minimum, or neither at each of these values. Justify your answers. (b) On what interval
1.) determine lim An= (n^2-11n+22)/(3n^2+29n+19) 2.) sketch graph 2x^2-4x+y^2+4y=10
Prove that if Series An (small "a", sub "n") is a conditionally convergent series and r is any real number, then there is a rearrangement of Series An whose sum is r. [Hints: Use the notation of Exercise 39 (I'll show below). Take just enough positive terms An+ so that their sum is greater than r. Then add just enough negati
1. DERIVE EQUATION 6-15 2. DERIVE EQUATION 6-48 AND 6-54 3. SOLVE ALL PROBLEMS SHOWN BELOW: 67. Water at 20°C flows through a smooth pipe of diameter 3 cm at 30 m3/h. Assuming developed flow, estimate (a) the wall shear stress (in Pa), (b) the pressure drop (in Pa/rn), and (c) the centerline velocity in the pipe. What is the
(See attached file for full problem description) --- 1) Consider the following function: a) f (x) = 9x2 - x3 b) f (x) = x + 1 x - 2 c) f (x) = x2/3 (x - 5) for each of the above functions complete the following table. Show the work to justify your answers below the table. f(x) is i
Using the given parameters, find the equation for the plane. Please show all work and a diagram if possible. Thank you. The plane through (1, -1. 3) parallel to the plane 3x + y + z = 7
In a backyard, there are two trees located at grid points A(-2,3) and B(4,-6). a) The family dog is walking through the backyard so that it is at all times twice as far From A as it is from B. Find the equation of the locus of the dog. Draw a graph that shows the two trees, the path of the dog. and the ralationship defining
6) If a nation's consumption function is given by : C(I) = 0.3I + 0.8 √I + 6 where I is national income, measured in billions of dollars a) Find the nation's marginal propensity to consume b) Find the nation's marginal propensity to save c) Evaluate the marginal propensity to save when I = 64
3) A wholesaler that sells computer monitors finds that selling price "p" is related to demand "q" by the relation p=280 - .02q where p is measured in dollars and q represents number of units sold a. Find the wholesaler's Revenue function as a function of q, using Revenue = (price) (quantity) b. Find the expression for Mar
We use the notation X ~N(μ, σ2) to indicate that the density function for the continuous random variable X, fx(x), has the form .... (a) If X ~N(μ, σ2) show that..... (Hint: you will need to know how to find the density function for X ? μ from the density function for X). (b) If ...., and X1 and X2 a
1. (a) Find the eigenvalues and eigenfunctions of the boundary-value problem. x2y'' + xy' + λ y = 0, y(1) = 0, y(5) = 0. (b) Put the differential equation in self -adjoint form. (c) Give an orthogonality relation. 2. Hermite's differential equation y'' -2xy' + 2ny = , n =
Calculate the unique solution for 7e^x in the following non-homogeneous second-order linear equation, showing all the steps. d²y/dx² + 5dy/dx - 6y = 7e^x
Please find the particular solution for xe^x in this problem and show all details. d²y/dx² - y = xe^x
The hemisphere is given by f (x,y) = sqrt 64 - x^2 - y^2. Sketch a contour map for this surface using the level curves corresponding to c = 0,1,2,3,4,5,6,7,8 Since this is an example shown in the book, I can see that when c = 8 you draw a circle with a radius of 8 and when c = 0 you have a point at the center of the circle.
The differential equation is: d²y/dx² - y = xe^x For the first part of the general solution, I got y=Ae^x + Be^-x where a and b are constants. Now I need to find the particular solution. Thanks.
Please see the attached file for the fully formatted problems. Please do problems 3 - 8, 10, 12, 14, 16 - 40 even, 42 ,44,45-49, 54 - 60 odd.
Please find the general solution of the nonhomogenous second order linear differential equation below by following these steps: 1. Find the general solution y= C1y1 + C2y2 of the associated homogenous equation (complementary solution) 2. Find a single solution of yp of above.(particular solution). 3. Express the general so
Find the particular solution of the differential equation : y=C(e^(-2x))sinx + C(e^(-2x))cos x y(0)= 1 y'(0)= 0
Find the particular solution of the general equation below, given the initial conditions. Please show all details in the solution, simplifying if possible. Thank you. y=C(e^(-2x))sinx + C(e^(-2x))cos x y(0)= 1 y'(0)= 0
Please find the particular solution of the differential equation below satisfying the given initial conditions. The equation needs to be put in standard form (s² + bs + c = 0). The roots need to be found, and then plugged into the appropriate general formula that satisfies whether b² + 4c is less than, greater than, or equa
Use a graph and level curves to estmate the local maximum and minimum values and saddle points of f(x,y) = x^3 - 3*x + y^4 - 2*y^2; then use calculus techniques to find these values precisely.
At time t = 0 a baseball that is 5 feet above the ground is hit with a bat. The ball leaves the bat with a speed of 80 feet per second at an angle of 30 degrees above horizontal. a) How long will it take for the baseball to hit the ground? b) Use the result in part a to find the horizontal distance traveled by the ball. Ple
1. For a thermodynamic process involving a perfect gas, the intial and final temperatures are related by: where is the specific heat capacity of the gas, is the change of entropy and and are the initial and final temperatures of the process. Determine the value of if and . 2. The overall efficiency of a gas turbi