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List these six partial derivatives for z = 3 x2 y + cos (x y) –...
Find a plane containing the point (-6,-5,2) and the line of intersection of the planes −7x−y−7z=−55...
Consider the function f(x)=5x−4 and find the following: a.) The average rate of change between the...
Consider the double integral R ???(? − ?) ???(? + ?) ?? ? where ? is...
f(x,y) = x2 y – 4 x y3 + ex+ y evaluate f(x,...
Use Calculus to find the open intervals on [0, 2pi) for which the function f(x) =...
Convert the cylindrical coordinate (4, n/3 , −2) into rectangular coordinates
Find the centroid of the region that is bounded by the line Y = 3X, the line...
In a murder investigation, the temperature of the corpse was 34°C at 1:30pm and 25°C 2...
A cable runs along the wall from C to P at a cost of $6 per...
Find derivatives (Please show work!) 1. f(x)=ln(5x^3) 2. f(x)=(ln^3)x 3. f(x)=e^(5x2+2) 4. f(x)=xe^2x 5. f(x)=xlnx
Let f(x, y) = sin x √y. Find the Taylor polynomial of degree two of f(x,...
1. At x = 1, the function g( x ) = 5x ln(x) − 3x is...
In Exercises 16-25, use any method to solve each nonhomogeneous equation. y'''+3y''+2y'=cos(t) Answer is apparently y=(1/10)...
If f is a differentiable function such that f ' ( x ) ≥ 8 ,...
3. The growth rate of Escherichia coli, a common bacterium found in the human intestine, is...
6. Metro Department Store found that t weeks after the end of a sales promotion the...
How to know that an integration should be solved by parts just by looking at the...
Find the directional derivative of the function f(x,y,z)=ln(x2+y2−1)+y+6z at the point (1,1,0) in the direction of...
Find the absolute extrema (absolute max/min) of ?(?, ?) = ?? − ? − 2? +...
Suppose the motion of a weight attached to a spring is given by the differential equation...
Consider two particles moving in the xyxy-plane according to parametric equations. At time tt, the position...
Find the point with x ≥ 0 on the parabola y = (1/8)x^2 − 5 that...
The cost of fuel to propel a boat through the water (in dollars per hour) is...
Use the method of Lagrange multipliers to set up the system of equations to find absolute...
find the line integral (total work) of the vector forces field f over the curve c...
evaluate integralusing trigonometric substitution sqrt(4x^2+1)dx
Explain how x + y = (x'y')' follows from de Morgan's law.
1. If f (x)= ln(3x^2 -2x +9), find the absolute minimum and absolute maximum on [-2,2]...
Suppose a pottery sells teapots and mugs. They can make a profit of P(x,y) = x^(3/2)*y^(1/2)...
The Maynard Smith and Slatkin model describes population growth. For specific values of its constants, the...
Using undetermined coefficients, what is the form of yp in the differential equation y''-3y'+2y = x^2...
Consider the equation y'' + 4y = 0. a) Justify why the functions y1 = cos(4t)...
f(x)=(-6x^2+2)^8(-9x^2-2)^13 find f’(x)
Find two unit vectors orthogonal to both given vectors. i + j + k, 3i +...
4 terms of a sequence of partial sums are given by: {Sn} = {27, 45, 57,...
A tank contains 1000 L of brine (saltwater) with 15 kg of dissolved salt. Pure water...
The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by x = (91 −...
1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and...
Find the general solution of the equation. y''-3y'+2y=e^3t
Given the differential equation to the right y''-3y'+2y=0 a) State the auxiliary equation. b) State the...
Find the dimensions of a rectangle with area 1000 ?2 whose perimeter is as small as...
Find the maclaurin series for f(x)=-3cosx
Consider the function ϕ(x,y) = x2 + y2. (1 pt) Find the gradient field for ϕ(x,y)....
what does a derivative tell us? F(x)=2x^2-5x-3, [-3,-1] F(x)=x^2+2x-1, [0,1] Give the intervals where the function...
Evaluate the line integral, where C is the given curve. ∫C xyz2 ds, C is the...
1-Find the area of the region between the graphs of f and g, where f(x) =...
Find the absolute maximum and minimum values of each function over the indicated interval, and indicate...
The position of a particle is given by s = f(t) = t^3 − 6t^2 +...
Use the Laplace transform to solve the given system of differential equations. dx/dt=x-2y dy/dt=5x-y x(0) =...
2. a. Given u = (9,7) and v = (2,3), find the projection of u onto...
1. a) A cylindrical length of wire has a radius of 4 mm and a length...
The cost of gas to tow a trailer, in dollars per hour, is proportional to the...
Let X and Y be independent and normally distributed random variables with waiting values E (X)...
A particle is moving along a straight line and has acceleration given by a(t) = 20t^3+12t^2}....
*** please do not use answer to the same question that was posted earlier today. I...
A reservoir in the shape of an inverted cone is filled to the top with water...
Use the first derivative test to determine the relative maximum or minimum values (if any) of...
) Consider the function f(x,y)=−2x^2−y^2. Find the the directional derivative of ff at the point (1,−3)(1,−3)...
The curve x = sqrt( (2y-y ^ 2) ) with 0 <= y <= 1/2 is...
According to 2012 estimated data, the USA has a Gini index of 47.1, the UK has...
\sum _{n=1}^{\infty }\left(\frac{3}{2^n}+\frac{8}{n\left(n+1\right)}\right)
Use the Chain Rule to evaluate the partial derivative ∂g/∂u at the point (u,v)=(0,1), where g(x,y)=x^2−y^2,...
find the equation of the tangent line when r=sqrt(sin0cos0) when 0(theta)=pi/4
Let f(x,y,z)=6xy−z^2, x=6rcos(θ), y=cos^2(θ), z=7r. Use the Chain Rule to calculate the partial derivative. (Use symbolic...
6. Evaluate Z 1/sqrt(x^2-9)dx
1) show that f(x) = x^3 -5x^2 + 9 satisfy the conditions of the mean value...
Given that f(x) = 2x3-3x2-72x, determine which x-values correspond to local minimums. 1) Local minimum at...
Find the Maclaurin series and associated radius of convergence for ?(?) = ln(2 − ?)
Test the series for convergence or divergene Σ infinite n=1 (-1) ^n 2^n/n!
a rectangle storage container with an open top is to have a volume of 16 cubic...
Use the Divergence Theorem to evaluate∫∫SF⋅dS where F=〈7xy^2,7x^2y,5z〉 and S is the boundary of the region...
Find the arc length ? = 1/2(? ^3/2) − 1 interval [2,6]
The present value of a sum of money is the amount that must be invested now,...
Let f(x,y) = 9y^2 −(3x^2)y denote the temperature at the point (x,y) in the plane, and...
Let R be the region bounded by 6 cos x, y = e^x , x =...
Find the degree-2 Taylor polynomial for the function f(x, y) = exy at the point (4,...
f(x,y)=x2+xy+y2+2x-5y+5 Find the local Maximum(?,?). The local maximum value is/are (?)Find all the local maxima, local...
The continuous function has exactly one critical point. Find the x-values at which the global maximum...
Find a formula for the nth partial sum Sn of the telescoping series: Then use Sn...
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