Use Green's Theorem to evaluate the line integral. S 2xy dx + (x + y) dy C: boundary of the region lying between the graphs of y = 0 and y = 1 - x²

Q: Find 3838 Əw Əv Əw - Əv y when u = 0, v = 0 if w=x² + −, x=3u - 6v + 1, y = 6u +3v - 3. |u= 0, v = 0…

A: Find

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Q: Which of the following vector fields are conservative? (i) F(x, y) = (6x³y5 + 9)i + (5x6y4 + 3) j…

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Q: √x csex² not x² dx 2

A: Consider the integral

Q: 5 Evaluate f de using the Fundamental Theorem of Calculus, Part 2. Use exact answers only. Use…

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Q: 8. Describe the domain for h(x) = √70-9x - x²

A: To describe the domain for .

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A: We have to solve the given initial value problem.

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A: Given,.

Q: A. B. Explain how you could use the graph of y=x² to graph -1 y=x². Sketch the graph of y=x².

A: graph of  from

Q: Evaluate the line integral L = = √ [a²y dx + (x² − y²) dy] over the given curves C' where (A) C is…

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Q: g. Σ. (3) n2 in=1 72

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Q: Let y = 3e¹ 2x³+e-4z. . Which is y'? You will need to simplify to find the answer.

A: The given function is

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A: The given expression is

Q: 364. lim x²/x 20+0

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A: Given In an opinion poll, 715 or 63% of people interviewed were opposed to the issue asked.Let…

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Q: A farmer has 2000 ft of fencing and plans to construct a rectangular pen. Find the dimensions of the…

A: Given data: The total length of fencing is 2000 ft.

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

A: The given function is.The aim si to verify the Rolle's theorem on the given interval.Rolle's…

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Q: Sketch a graph of x = 3t-1, y=t-1. -5 -4 -3 -2 -1 Clear All Draw: 5 4 3- 2 1 -1 -2 -3 -4 -5 1 2 3 4…

A: Sketch the graph and orientation of the parametric equation.

Q: Find the equation of the tangent line to y = (x³ + 2x + 3) eª at the point where x=0. The equation…

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Q: S (੮)

A: given point in 3 dimension(a) (2,5,3)(b) (-6,3,2)

Q: Solve for x: 3e³-5 = 4 Just enter the number and give a decimal (rounded) answer to 4 places.

A: To solve for .

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) (3-4x) (3 - 4x)¹0 dx

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Q: Compute the line integral fx²yds, where C is the arc of the circle x² + y² = 9 in the first…

A: To find:-The line integral, where C is the arc of circle  in the first quadrant.

Q: 1. y'(t) − y(t) = 1, Ans. y(t) = e' - 1 y(0) = 0

A: given IVP

Q: g(x) = * (4 + sin(t)) dt

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Q: Consider the function f(x) = 14x - 4sin-¹. Find the critical number(s) off in the interval [-1,1].…

A: The given function is

Q: Question 5 (a) Determine the partial derivatives of the following functions with respect to each of…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: The following table shows the total sales, in thousands, since a new game was brought to market.…

A: Part (a): The data appear plotted with dots below:

Q: Sketch the graph of the following, given y = f(x). y = f(x) -4 2 Use the graph to answer this y =…

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Q: Consider the following polynomial function. f(x)=(x+1)2(x−2)5(x−3) Step 2 of 3:  Find the…

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Q: Let f (x) = log2(x) + 2 and g(x) = log2(x3) – 6. Part A: If h(x) = f (x) + g(x), solve for h(x) in…

A: This is Question of calculus.Here logerithmic equation function is given.We have to summation of…

Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = sin²(x) = cos(2x), 0≤x≤…

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Q: 5nti sign Σ 5² = 25 25 = 25 2+1 5° 3 2. Use the Ratio Test or the Root Test to determine if the…

A: Note:-Since you asked multiple subparts,according to our policy we can solve only first three…

Q: Graph the function: f(x)=(x-3)² 4-X if x4

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Q: eral Antiderivative) Evaluate the following indefinite integral: πχ' cos (x³) dx

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Q: Evaluate the integral by interpreting it in terms of areas. 3 6.³ |2x - 3| dx

A: Simplify the absolute value of expression under integrand.

Q: example 1- Find the linear approximation to f(x)=√√2x+1 at x = 4, then use it to approximate he…

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Q: Question 3.1. Use integration by parts to solve the given indefinite integral and thus evaluate…

A: By using integration by parts to solve the given indefinite integral and thus to evaluate…

Q: Given the function f'(x) = −x³ – 6x² + 72x, determine all intervals on which f is decreasing.

A: If f'(x)> 0 in an interval I then f(x) is increasing on interval I.If f'(x)<0 in an interval I…

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Q: Find the values of the six trigonometric functions of 8. (If an answer is undefined, enter…

A: To find the values of the six trigonometric functions of .Function value: Constraint:  lies in the…

Q: x^1/3(x+3)^2/3 find critical points, increasing and decreasing, inflection points, local minimum and…

A: f(x)=

Q: 2. Find the Wronskian of the following: b) (sin cos

A: We have to find the Wronskian for the given function.