Calculate the curl of the vector g = (x−y) ax+(y+x) ay, and visualize it. Explain what does "curl of vector field" mean, in your own words. When does it equal zero?

Q: f(x,y)= x/x+y.  Find fxx, fyy, fxy, fyx.

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Q: Find the first and second derivatives of the function.

A: Given  fx=x8x+5 Using quotient rule to find the derivative of f(x)         fuv=v.u'-u.v'v2…

Q: 16. Write the expression below in standard form by completing the square and express the vertex.…

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Q: Find the derivative of the function. 경기 dx y= || - 11 잤

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Q: Find f[g(x)] and g[f(x)]. f(x)=√x+3, g(x) = 12x² - 7 f[g(x)] = g[f(x)] =

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Q: 3. Let (an) and (b) be sequences. Suppose that (an) converges to 0. (a) Using the definition of…

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Q: Evaluate the integral and check your answer by differentiating. 4x6 / 2² +10²-1 dr == +C

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Q: Differentiate the following function. y=ets dy dx = d dx )= lets

A: To find the derivative of the given function.

Q: Use the product rule to find the derivative of the following y = (x+1) (3/x+7) dy dx =

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Q: A company uses the model R(x) = 300x²x³ 10000 to relate its revenue, R, in thousands of dollars, to…

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Q: Find the derivative. y = In (6-5x) dy dx ㅁ

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Q: Find all the inflection points of the function. += 75

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Q: Determine the set of points at which the function is continuous. F(x, y) = arctan(x4 + √y) D = {(x,…

A: The answer is in step 2.

Q: What is the exact value of the trigonometric expression? 2π 3 tan - sec (-7) Ίπ 4 State your answer…

A: Explanation of the answer is as follows

Q: Find the derivative. y = 9~x O A.dy dx OB. dy 기 dx OC. dy 경기 경기 dx OD. dy dx =g-x = - gx = In9(9-x)…

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Q: Differentiate the function. R(a) = (6a + 1)² R'(a) = 12 X

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Q: A) f(x)=12+9x-3x²-x³ [-3,1]

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Q: whats the answer to g'(8)

A: see below the answer and explanation

Q: Let f(x) = −3x² + 1 1 X3 + −xª. Find all local and absolute maxima and minima of f.

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Q: 9. A ball is thrown across a playing field. Its path is given by the equation = −0.005x²+x+5, where…

A: A ball is thrown across a playing field. Its path is given by the equation y=-0.005x2+x+5, where x…

Q: Find the radius of convergence and the interval of convergence. Σ()+ Radius of convergence: (x + 7)…

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Q: 7. Use the graphs of the function below to determine the domain and range of the function and the…

A: Please see the below answer.

Q: Find the error in the following work. Dx 2x+5 2 x-1 = || 11 (2x + 5)(2x) - (x² − 1)2 (x²-1)² 4x²…

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Q: 1. Suppose that in a monopoly market the total cost per week of producing a high- tech product is…

A: Given :C=3600+100x+2x2p=500-2x

Q: # 4 y = f(x) X poncists of a quarter

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Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

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Q: 1. Find the general solution to the differential equation 2x(y+1)- yy' = 0.

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Q: Let -2x² - xy +10y² − 15x + 12y — 22 = 0. dy dx Use partial derivatives to calculate at the point…

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Q: Write a differential formula that estimates the given change in volume. The change in the volume V =…

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Q: For each of the given functions f(x), find the derivative (ƒ-¹)'(c) at the given point c, first…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Solve. 27(9) 32x+34 = 16 X= Round to 4 decimal places.

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Q: 1. Find the equation of a curve for which y" = 6x and which passes through the points (0,2) and…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Chain Rule (Multiple independent variables) Let w(x, y, z) = √² + y² + 2² wherer = -7re', y = -te'…

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Q: Find the derivative of the function. F(x) = (4x + 2)³ (x² - 5x+2)4

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Q: 23. What are the roots of the auxiliary equation corresponding to the DE y(4)+3y"+6y" +5y+3y = 0 (A)…

A: As per guideline we can solve maximum one question you can repost other question

Q: Find the volume of the solid in the first octant bounded by the sphere x2 + y² + ² = 4, the ㅠ…

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Q: The vectors u, v and w are shown in the diagram below. 80° V 40° Given Jul = 6, |v| = 8 and [w] =…

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Q: Show that f(x, y) = e³x sin 3x satisfy Laplace's equation.

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 9x [e³ dx =…

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Q: A book store manager observes that the number of magazines sold seems to vary inversely as the price…

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Q: Find the derivative of the following function. y=107x+4

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Q: increasing decreasing g(x) = x4 - 18x² + 5

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Q: Let z(x, y) =xy where x=rcos(-40) & y =rsin(20). Әх ду Әх Ər' ar' 20 > Calculate дz dr Oz 20 amd Oz…

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Q: Corey spies a bald eagle in a tall tree. He estimates the height of the tree to be 80 feet and the…

A: Here, We will use trigonometric ratios to find the desired value.

Q: Find the derivative of P=155e^0.18t

A: p=155e0.18td dt(et)=et

Q: Determine the x-value of all critical points for the following function. 2 3x² X-5 f(x) = 3x² X-5…

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Q: 9. 7-6-5-4-3-2 -3-2-1\0/ 1\2/3 익

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the derivative of the function, using chain rule. f(?) = cos(?2)

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Q: b) f(x) = x² - 12x + 55 on the interval [6, ∞); c = 20. Note that f(7) = 20. a = (ƒ-¹)'(c) =

A: Please see the below picture for detailed solution.

Q: Take a standard 8.5 in. by 11 in. page of paper. You're going to cut square corners of equal size…

A: According to question,We have,Dimension of paper : 8.5 in. × 11 in.