Find the curl of the vector field at the given point. F(x, y, z) = x²zi - 2xzj+yzk; (9,-9, 9) curl F =

Q: akes the following function continuous on (-∞, ∞).

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Q: Use polar coordinates to set up and evaluate the double integral f(x, y) = x + y, R: x² + y² ≤ 64, x…

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Q: A textbook company publishes computer, educational and utility type of books. Their business…

A: We have to find how many educational books should the company publish annually for maximum profit.

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: Determine whether the vector field F is conservative. F(x, y, z) = ye²i + zexj + xe k conservative…

A: We have to check if F is conservative or not.

Q: Average Cost The total daily cost (in dollars) of producing a mountain bikes is given by C(x) =…

A: Given, C(x)=7000+4x+0.7x2

Q: elax upx dx

A: ∫1xlnx23dx

Q: 1) y" - 36y = 0.

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Q: Consider the following function. f(x) = 4x² - 7x² Determine whether the function is even, odd, or…

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Q: Find the Jacobian (x, y)/(u, v) for the indicated change of variables. x = 3u - v, y = 2u + 6v a(x,…

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Q: Determine whether the vector field is conservative. F(x, y) = xe+²2y (2y + xj) conservative O not…

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Q: 15) I What is the average rate of change of f(x) = from x = -2 tox = 4? x-s X+3 b 24 7 M C. d. 25 21…

A: We know that the expression for the average rate of change between the interval x2≤x≤x1 is: Average…

Q: Evaluate the integral. (Use C for the constant of integration.) tan(x) cos(x) dx

A: ∫tan8xcos9xdx

Q: x, y) u, v) S S u area of the ellipse using the indicated change of variables. 1 V S S 2 u u

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Q: Why is the Second Derivative Test inconclusive when f"(c) = 0? Explain. Please use clear…

A: This is a problem related to derivative. Please follow the procedure given below.

Q: Write an equation for a rational function with: Vertical asymptotes at x = -4 and x = 2 x-intercepts…

A: We need to write an equation for a rational function with : Vertical asymptotes at x=-4 and x=2…

Q: Integrate f Osin-15x+C ○ -sin-¹5x + C 1 dx 1-25x2 - 5 H|K sin ¹5x + C cos ¹5x + C

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Q: 2. (x + y) dx + (3x + 3y − 4) dy = 0

A: The given differential equation is;  (x+y)dx+(3x+3y-4)dy=0.

Q: Use the limit definition of the derivative to calculate the derivative of f f'(x) = f(x)=-3x³ - 2x +…

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Q: A rectangular box with no top is to be built from 1452 square meters of material. Find the…

A: We use the method of langrange multipliers to solve the given problem.

Q: calculation for P.I ур cos²x D²+1 2 2 cos²x D² + 1 1 {3 2 21 - 1+ cos2x D² + I HOW DID HE GET THE…

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Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

A: We will solve.

Q: Find the real roots of the equation B 244

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: y" - 12y' + 36y = 12x + 3 nd the complementary function for the differential equation. _(x) nd the…

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Q: Find the domain of the function. 7 |x²-161 g(x)

A: Domain : It is the set of all real numbers for which the equation is defined.

Q: Sketch the solid whose volume is given by the iterated integral and rewrite the integral using the…

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Q: Find the general solution of the given second-order differential equation. 25y" - 15y' - 4y = 0…

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Q: s help A

A: calculus

Q: 8. Calculate the following limits. In z lim → 2²-1 (b) [ 1³-1³ 0 e + cos2-1-2 lim

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Q: A math teacher won a lottery that pays $1,000 per month for the next 20 years. But, he prefers to…

A: To find out the amount that the teacher will accept now.

Q: Find the general solution of the given higher-order differential equation. y"" + 4y" - 9y' - 36y = 0

A: Follow the procedure given below.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Use a double integral to find the volume of the indicated solid. X 6 N 2 40 30 20 10 z = 36- y² y =…

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Q: Sketch the region of integration. [ [² x√ 1 + y³ dy dx

A: The answer as follows:

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: We need to find y2.

Q: Sketch the region R and evaluate the iterated integral IT x²y² dx dy y 10 8 6 2 y 10 8 00 6 4 2 [[…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = (1, 5, 5)

A: Follow the procedure given below.

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Given solution is y=C1+C2x+C3e4x

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A: Given that      differential equation   6y''+y'-y = 0      ,        y1= ex3         and…

Q: Sketch the image S in the uv-plane of the region R in the xy-plane using the given transformations.…

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Q: Evaluate the iterated integral by converting to polar coordinates. -x² IT (x² + y²) dy dx dr de-

A: We can evaluate the given iterated integral.

Q: Evaluate the integral of x cos 2x dx with limits form 0 to pi/2. (A) -3/4 B 0.75 C -0.5 D 1/2

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Q: Determine the general solution of the given differential equation. y"" - y = 11 sint NOTE: Use C₁,…

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Q: Use the one-to-one property of logarithms to solve. (Enter your answers as a comma-separated list.)…

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Q: need the answer quickly

A: simplification

Q: 2. Consider finding the root of f(x) = e*(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

A: Concept: Bisection method: To determine the roots of a polynomial problem, utilize the bisection…