Determine if the field F = 2yz i + 2xz j+ 2xy k is conservative or not conservative.

Q: x² The rectangles in the graph below illustrate a right endpoint Riemann sum for f(x) = on the…

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Q: A particle is moving with the given data. Find the position of the particle, s(t). = 5 cos(t) 4…

A: given,  a(t)=5cos(t)-4sin(t)given conditions,  s(0)=0 and v(0)=8formula of integration→(i)…

Q: Write the given expression as an algebraic expression in x. cos(2 tan-¹(x)) 1 -2x² (1+x²)² X

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Q: The graph of f is shown below. (Click on a graph to enlarge it.) Evaluate the following integrals by…

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Q: Solve the linear programming problem. Maximize and minimize z = 2x + 3y Subject to 2x + y 2 30 x+2y…

A: Maximize and Minimize z = 2x + 3y Subject to : 2x + y ≥ 30 x + 2y ≥ 24 x, y ≥ 0 To draw constraint…

Q: A manufacturer of ski clothing makes ski pants and ski jackets. The profit on a pair of ski pants is…

A: Given Profit on a pair of ski pants is $2.00  and on a jacket is $1.50. There are 60 minutes of…

Q: 77. Simple epidemic. An influenza epidemic has spread throughout a community of 50,000 people at a…

A: Total population =50,000Let y be number of people infected then 50,000-y non infected people

Q: The Intermediate Value Theorem guarantees the existence of at least one real zero of the polynomial…

A: The Intermediate Value Theorem (IVT) is a fundamental theorem in calculus that relates to the…

Q: 1. The series meets the conditions to use the ratio test, and lim 11 00 A. M8 an converges n=1 B.…

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Q: Divide f(x) by d(x). Your answer should be in the following format: R(x) f(x) = Q(x) + d(x) (x) =…

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Q: let f(x) = 1 x + 6* (a) Determine the difference quotient and simplify. f(x+h)-f(x) h (b) Determine…

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Q: Find the equation of the tangent line to f(x) = x² at x = 1. 4 3 2 1 (a) y= -1 -1 -2 -3 -4- 1 a

A: e

Q: 7. Part 2. Evaluate each definite integral using the Fundamental Theorem of Calcul TT/2 a) √ (3e* +…

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Q: Find f. f(t) f'(t) sec²t, -π/2 < t < π/2₁ = 10 cos t + sec f(π/3) = 1

A: f'(t)=10cos(t) + sec2(t)  -π/2&lt;t&lt;π/2 Also, f(π/3)=1

Q: Use the definite integral to find the area between the x-axis and f(x) over the indicated interval.…

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Q: 6. Evaluate the indefinite integral (3x² − 2)(x³ − 2x)dx

A: Need to perform the indefinite integral after simplifying the expression.

Q: Q.6 Given the functions: f (x) = x 2 - 9 and g (x) = x-3, what is (f / g) (x)?   x + 3 x - 3 x -…

A: We have given f(x) and g(x) and we have to find (f/g)(x).   According to our guidelines we can solve…

Q: (a) Find the unit vectors that are parallel to the tangent line to the curve y = 8 sin x at the…

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Find the area of the region enelosed by the curves y=4-x^(2) and y=-1.

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Q: 1. The plane 3x - 3y -z = 4 intersects the paraboloid z = 1² + y² in an ellipse. Use the method of…

A: Here we can find the points on the ellipse where the paraboloid intersects the plane by setting the…

Q: Two systems of equations are given below. For each system, choose the best description of its…

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Q: 1. Find the following for the function f(x, y) = 3x³y² - 5x + 26y - 9.

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Q: Use the definite integral to find the area between the x-axis and f(x) over the indicated interval.…

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Q: 5. Use the second-derivative test for local extrema to indicate any local extrema and saddle points…

A: Given   fx,y=x2+y2+6x-8y+10 Concept: The Second Order partial derivative test Let fx,y be a function…

Q: f(x, y, z) = x + 2y - 2z, A) Maximum: B) Maximum: C) Maximum: D) Maximum: 1 at 8 at 1 at 9 at x² +…

A: fx,y,z=x+2y-2zgx,y,z=x2+y2+z2-9

Q: ing the graph shown a. Find g(1) b. Solve g(x) = 1 C. Find g(1) d. Solve g(x) = 1 -2 -1 g(x) 2 1 -1…

A: Here given that a graph of g(x) and x and we find value of g(1) and other.

Q: Determine whether the statement below is true or false. If the statement is false, make the…

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Q: Consider the function f(x) = - +4. In this problem you will calculate √(- ³²3² + +4) dx by using the…

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Q: -x² 5 , and it is [select an answer] The rectangles in the graph below illustrate a left endpoint…

A: It is given that the function is fx=-x25+2x and the interval is 3,7. It is required to find left…

Q: 5. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. a) S…

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Q: Use the regression function of a graphing tool to find the least squares regression line for the…

A: We have to find the least squares regression line.

Q: Find the area of the region bounded by the curves y=xe^(−0.4x), x=5, and y=0

A: y=xe-0.4x, x=5 , and y=0  Find the area of the region bounded by the curves

Q: 1. Find the following for the function f(x, y) = 3x³y² — 5x + 26y - 9. a. f(1,2)= b. fy(x, y) =

A: To find the following for the function fx, y=3x3y2-5x+26y-9. (a) f1, 2=? (b) fyx, y=?

Q: 4 √In x 8) Set x dx

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Q: Pollution levels in a lake have been modeled by the equation x = 0.03 + 0.18e−0.35t where x is the…

A: The given equation x=0.03+0.18e-0.35t, where x is the volume of the pollutants and t is the time in…

Q: Use Newton's method to find all roots of the equation correct to six decimal places. (Enter your…

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Q: A manufacturer of corrugated metal roofing wants to produce panels that are u = 24 in. wide and 2…

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Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

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Q: For the following polynomial function f(x)= x³ - 3x² - 2x + 2, find the lower bound within which all…

A: We have to find the lower bound of the interval in which the roots of the polynomial lie.

Q: Write the rule of a function that gives the perimeter of a rectangle of length L and width w. P(L,w)…

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Q: Suppose f is continuous on an interval containing a critical point c and f''(c) = 0. How do you…

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Q: Sketch the region R whose area is given by the iterated integral. 16 *16 - X [²[* y 8 6* [* d 16 14-…

A: To sketch the region R whose area is given by the iterated integral: ∫08∫0x dy dx + ∫816∫016-x dy dx…

Q: Evaluate f -dx 3 x²+3x¹ x² 1

A: Integral

Q: Find the exact area of the region that lies beneath the curve y=7x−4,   1≤x≤6…

A: y=7x−4,   1≤x≤6

Q: Let f(x, y) = y²x², and let D = {(x, y)² + 4y² ≤ 4}. (a) Find the absolute maximum and minimum…

A: (a) To find the absolute maximum and minimum values of f(x, y) on D, we need to find the values of…

Q: Consider the family of functions given by: f(x) = 5x - 5A³In(x) where A is a nonzero constant.…

A: We need to solve function problem.

Q: Evaluate S 1 d dx /1+x²

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Q: p(t) = 1 √√/t²

A: Here we have to find the anti derivative i,e integration of p(t)Given p(t)=1t23or, p(t)=t-2/3

Q: 20. The parametric chain rule states dx II dy dt. Prove this statement. dx dt 21. Explain how the…

A: (20)