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A thin plate covers the triangular region of the xy-plane with vertices (0,0), (1,1), and (−1,1)....
1) Find the absolute maximum value and the absolute minimum, if any, of the given function....
A large tank contains 100 liters of a salt solution with a concentration of 50 grams/Liter....
Let f(x,y)=e^(−5x)sin(3y). (a) Using difference quotients with Δx=0.1 and Δy=0.1, we estimate fx(3,2)≈ fy(3,2)≈ (b) Using...
F(g(x))=x^4 and G'(1)=2 find F'(g(1))
Show your complete solution. 1. Use Lagrange Multiplier to determine the dimensions of a rectangular box,...
I would like to create a rectangular vegetable patch. The fencing for the east and west...
If the instantaneous value of a voltage in an AC circuit of the communication system (at...
Find an equation of the plane that passes through the point (-1, -3, 1) and contains...
Use change of variables and the Jacobian to solve the double integral ∬ (? − 5?)√?...
Verify that the indicated function is a solution of the given differentialequation.x2y′′−xy′+ 2y= 0;y=xcos (lnx), x...
a. r=3 - 3cos(Θ), enter value for r on a table when; Θ=0, (π/3),(π/2),(2π/3),π,(4π/3),(3π/2),(5π/3) & 2π...
a). Find dy/dx for the following integral. y=Integral from 0 to cosine(x) dt/√1+ t^2 , 0<x<pi ...
1. Find the slope of the tangent line to r=2+sin3Θ at the point where Θ=pi/4 Θ=theta...
Problem 15: Find the taylor series for f (x) = cos (2x) around x = pi/4,...
Let h be the function defined by H(x)= integral pi/4 to x (sin^2(t))dt. Which of the...
find the maclaurin series for f(x)= (eX)-(e-x)/(2)
Examine ?(?, ?) = 2(?^2) − 4? + ?(?^2) − 1 for relative extrema.
A cup of tea is cooling in a room that has a constant temperature of 70...
1. Find the slope of the tangent line to r=2+sin30 at the point where Θ=pi/4 2....
You've decided to sell sweatshirts for the upcoming game. You project that at a price of...
Suppose that 6 J of work is needed to stretch a spring from its natural length...
5. Find the area bounded by the curves: two x = 2y - y^2 ; x...
(1 point) A fence is to be built to enclose a rectangular area of 210 square...
This is a sample on the derivatives of the exponential and logarithmic functions. All questions ask...
Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces....
Use Gauss-Jordan method (augmented matrix method) to solve the following systems of linear equations. Indicate whether...
Part A: Compute the derivative of ?(?)=?^15/2 Part B: Compute the derivative of ℎ(?)=5?^−2 + 2...
Suppose that two boats leave a dock at different times. One heads due north, the other...
On what intervals is the function f(x)=x^4-j4x^3 both decreasing and concave up? x<3 x<0 or 2<x<3...
Find the location of the critical point of the function f(x,y)= kx^(2)+3y^(2)-2xy-24y (in terms of k)...
A company wants to manufacture a rectangular planter box of volume 12 litres (12, 000 cm3...
please only answer if you can do all parts, I also included my answer but they...
Find the area of the surface The part of the parabloid z=4-x^2-y^2 that lies above the...
Let F~ (x, y, z) = x cos(x 2 + y 2 − z 2 )~i...
find the particular solution for the following initial value problems A) x dy/dx +2y = x...
Determine whether the lines l1: x = 2 + u, y = 1 + u, z...
Find the Maclaurin series for f(x) = ln(x + 3).
A 225 meters squared rectangular pea patch is to be enclosed by a fence. What should...
Let R be the region between parabolas x=1-y2 and x=3(1-y2). Find a planar transformation that transforms...
Certain radioactive material decays at a rate proportional to the amount present. If you currently have...
Find the angle between the curves y = cot x and y = tan x where...
Using Lagrange multipliers Minimize f(x,y,z)=x^2+4y^2+2z^2 subject to x+2y+z=10
Use triple integral and find the volume of the solid E bounded by the paraboloid z...
Let C be a closed curve parametrized by r(t) = sin ti+cos tj with 0 ≤...
Determine the open intervals on which the graph is concave upward or concave downward. (Enter your...
a rectangular box with no top and six compartments is to be made to hold a...
Find all relative extrema. Use second derivative test where applicable for ?(?) = 2 sin ?...
The cost in dollars of producing x units of a commodity is: C(x)= 920 + 2x...
How to find the first three terms of the Maclaurin Series for f(x) = sin(2*pi*x).
find the limit lim(x cos 1/x + sin23x3/tan3x2) lim(x->0) going to 0
The formula for wind chill C (in degrees Fahrenheit) is given by C = 35.74 +...
f(x) 4x(to the power 5) - 5x(to the power2"esquire ) - 2 on the interval [-2,...
Problem (9). Let R be the region enclosed by y = 2x, the x-axis, and x...
Why does the end point change when we take the integral or derivative of a power...
Evaluate the limit with either L'Hôpital's rule or previously learned methods. lim x→0 (5x-3x)/x
4. Let W be the three dimensional solid inside the sphere x^2 + y^2 + z^2...
An airline requires that the total outside dimensions (length + width + height) of a checked...
Use the function ?(?) = ?4 − 4?3 for questions 12 – 14. 12. Find where...
Find the area enclosed by the ellipse x^2/a^2 + y^2/b^2 = 1. What happens when a...
I would like to create a rectangular vegetable patch. The fencing for the east and west...
A company is designing an aquarium in the shape of a vertical cylinder for a client....
find the solution to the differential question. d^2y/dt^2 + 9dy/dt = 0 , y(0)=1, y'(0)=3
Let A be a real matrix of 7 × 5 format. Answer the questions following: (1)...
Find the average value of the function over the given interval and all values of x...
For the function below, find (a) the critical numbers; (b) the open intervals where the function...
Derivative for each function h(x)= x1/4 (x2+1)5 k(x) = (e3x) / (1-e-3x) m(x) = 2ln (...
A storage shed is to be built in the shape of a box with a square...
An oil refinery is located 1 km north of the north bank of a straight river...
Set up the integral. you do NOT have to integrate. A region is bounded by the...
Find the terms through x^5 in the Maclaurin series for the function f(x)=x^2tanx
Find the general solution and initial value solution: (cos x)dy = -2y2(tan x)dx, y(0)=1/6
You lean your 5 foot long ladder up against the wall. However, a cat decides to...
Determine if ∞∑ k=5 (3/((k−2)(k+ 1))) converges and find its value.
You want to mail a cylindrical package containing some gifts to your friend in California. Postal...
Q4. Given F = [x2 +xy,x2 +y2] and C is the square formed by the lines...
Sketch a continuous graph that satisfies each set of conditions. d) f"(x)=1 when x>-2, f"(x)=-1 when...
Suppose X∞ n=0 cnxn converges when x = −4 and diverges when x = 6. State...
A store can sell 20 bicycles per week at a price of $400 each. The manager...
For f(x,y,z) = sqrt(35-x^2-4y^2-2z) 1. Find the gradient of f(x,y,z) 2. Evaluate delta f(x,y,z) 3. Find...
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