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10.) (23 pts.) Verify the Divergence Theorem for P(x, y, z) = (y) i+ (—x) j...
Let f(x, y) = 2x^3y^2 + 3xy^3 4x^3 y. Find (a) fx (c) fxx (b) fy...
An open-top box has a square bottom and is made to have a volume of 50in^3....
Find the volume of the solid generated by revolving the following region about the given axis....
Find the vectors T and N and the binormal vector B = T ⨯ N, for...
Find an equation for the line L that contains the point the point P = (−1,...
Determine the value of the area formed by the figure limited by the functions y =...
1.) For y = f ( x ), the __________ from x = a to x...
Find parametric equations for the tangent line to the curve with the given parametric equations at...
Consider the vector a(t)=〈cost,sint〉 with components that depend on a real number t. As the number...
5. (a) Find the length of the given line, C, using calculus and the arc length...
5) If the instantaneous rate of change of the population can be given by 50 t...
determine the Maclaurin series of e^(-x^2)
Find the volume under surface given by f(x, y) = 9 −6yˆ2/xˆ2 and above the region...
Verify that the vectors a, b, and a+b, and, respectively, a, b, and a−b satisfy the...
Find the tangent plane and normal line to zy + 4x √ z − xˆ3yˆ2 =...
Calculate the following multi-variable limits if they exist limx,y→(2,1) xˆ2 − 2xy / xˆ2 − 4yˆ2...
A resistor R = 4 ohms, a capacitor C = 1F and an inductor L =...
What is the antigradient of the given gradient function \nabla f = (z, x, y)
find the length of the curve r(t)=(tsint+cost)i+(tcost-sint)j from t=sqrt(2) to 2
a trough is filled with a liquid of density 870kg/m^3.the ends of the trough are equilateral...
Use Euler's method with step size 0.2 to estimate y(3), where y(x) is the solution of...
3) The marginal cost for producing x items can be given by the formula: C ′...
Suppose a product's revenue function is given by R(q)=−7q^2+200q, where R(q) is in dollars and q...
1. Use cylindrical shells to find the volume of the solid generated when the region enclosed...
Write and evaluate the definite integral that represents the area of the region bounded by the...
Find the Taylor polynomial of degree 3, centered at a=4 for the function f(x)= sqrt (x+4)
Evaluate the given integral by changing to polar coordinates. R (5x − y) dA, where R...
You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc., and you wish...
Bismuth-210 has a half-life of 5.0 days. (a) A sample originally has a mass of 800...
If a rock is thrown upward on the planet Mars with a velocity of 15 m/s,...
Consider the following planes. 5x − 4y + z = 1, 4x + y − 5z...
given the polynomial function f(x)=x^2(x-3)(x+1) find x and y intercepts of f(x) and determine whether the...
Is the derivative of a polynomial is always a polynomial? what about the derivative of a...
Given: f(x) = x^3-3x^2 -9x + 1 which (if any) of the following statements are true?...
A patient is injected with a drug every 12 hours. Immediately before each injection the concentration...
A company estimates that the revenue (in dollars) from the sale of x doghouses is given...
From 1995 through 2005, the number v ogveterans (in thousands) receiving compensation and pension benefits for...
Find parametric equations for the tangent line to the curve r(t)= <t^7, t^6, t^5> when t=1
Convert equation from spherical to cartesian: 4−ρ2sin2ϕ−ρcosϕ=0
Identify which of the following are examples of y as function of x, and give a...
Find the slope of the tangent line to the given polar curve at the point specified...
1a.) Find the linearization of the function f(x) = (sin x+1)^2 at a = 0. 1b.)...
Find a Fourier Series expansion for the function f(x)= xcos(3x) on the domain from x =...
Consider the parabola given by the equation y = x2 − 5 4 . Let (a,b)...
A spherical balloon is being deflated at a rate of 8 cm3/s. At what rate is...
Evaluate F · dr, where F(x, y) = <(xy), (3y^2)> and C is the portion of...
Consider the function g(t) = 4 t e−t/2 . What is lim t→∞ g(t) ? One...
A. The derivative of f(x)=(5x3+4)(6ln(x)-2x) B. The derivative of c(x)=ln(4x3-x2)
a) Determine all x-values where the function has a horizontal tangent line. y=ln(1+sinx) b) The position...
At what point does the normal to y= (-1)+(4x^2) at (1,3) intersect the parabola a SECOND...
If x^3 +y^3 = 28, find the value of d^2y/dx^2 at the point (1,3).
Consider the ellipse r(t) =〈3 cos(t),4 sin(t)〉, for 0 ≤ t ≤ 2π. (a) At what...
Apply Lagrange multipliers to solve the problem. Find the dimensions of the box with a volume...
Find equations of the tangent lines to the curve y = x − 1/x + 1...
a. 6. Complete the following steps: i. Graph the point P(6, -2) ii. Graph another point...
A bakery works out a demand function for its chocolate chip cookies and finds it to...
A spherical tank with radius 2m is half full. Set up, but DO NOT evaluate, an...
Use the Laplace transform to solve the following initial value problem, y′′ − 8y′ − 9y ...
Sketch the graphs of the quadratics surfaces defined by the equations x = z2 - y2...
1. Find the radius of convergence for: ∞∑n=1 (n!)^2 x^n /(2n)! 2. Find all the values of...
The table below shows values for four differentiable functions. Suppose we know the following things: h'(x)...
find laplace transform without using known transform: f(t)=at+bcos(2t)
Find the curvature, k(t), of the following: r(t) = t i + t^2 j + e^t...
1. Find the derivative of the function. y = e−8/x 2. Find the derivative of the...
b) i) Find the residues of the function ?(?) = ?2+1 ?(?−6) at its poles in...
Suppose that f is a differentiable function and define g(x)=e^(2*f(x)+5x). Suppose that f(-2) = 1 and...
Consider the graph y=6x^(1/5)+x^(6/5) Determine: a) interval(s) on which it is increasing b) interval(s) on which...
Evaluate ∫ ?−2 / [(2?−1)^2 * (?−1)] ?x
Two motorcycles, travelling at the same speed, approach an intersection, one from the north and the...
A conical tank is 14m high and its diameter across the top is 10m. Water is...
Determine the equation of the normal to y2 = (x3/2-x) at the point (1,-1). [ANSWER: y...
Given the given cost function C(x)=2600+590x+1.2x2 and the demand function p(x)=1770 Find the production level that...
find the derivative of the functions T(theta)=cos(theta^2 + 3theta - 10) f(x)=(3x/(x^2-1))^3/2
2. Suppose that F(x,y) is a conservative vector field with potential function f(x,y). Suppose that every...
find the equation of a tangent line(s) to the curve with slope 5 f(x)=x^3 + 3x^2...
a) Let y be the solution of the equation y ′ − [(3x^2*y)/(1+x^3)]=1+x^3 satisfying the condition y...
1. Find and interpret f'(−2) f(x)=−2x^2−3x+4 f'(-2)= 2. Find and interpret f'(1)and f′'(1) f(x)= 2/x f'(1)=...
Calculate the trapezoidal sum for the function f ( x ) = x^ 2 over the...
Given: Sigma (infinity) (n=1) sin((2n-1)pi/2)ne^-n Question: Determine if the series converges or diverges Additional: If converges,...
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