= Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep safe. Since Dr. Jones is a mathematician, she suggests building fences described by y = 2x² and y x² + 2. Farmer Jones thinks this would be much harder than just building an enclosure with straight sides, but he wants to please his wife. What is the area of the enclosed region?

Q: 8. Evaluate F. dr using Stoke's theorem when F = (2xy — x²)ī — x² − y² )ī and C is the boundary of…

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A: Given :   xdx+sin2yxydx-xdy=0

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Q: 16. Given the graph of g(x), Draw the graph of g-¹(x). Show your strategy for drawing the graph of…

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Q: Solve the differential equation xdæ +sin? (%) [yda — xdy]=0 2x a. 4x In 2y + x sin (2²) = 0 O b. 4x…

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Q: ✓cos x lim x 0 1 cos x - -

A: The given limit is limx→01-cosx1-cosx

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Q: Which function has Maclaurin series (-1)"2""? n:o OAI OB 8. 2/7/2 Oc O D. TIZE D.E. 2

A: The given series: ∑n=0∞-1n2nxn

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Q: Evaluate the integral: (A) Which trig substitution is correct for this integral? 1 0x = -sec (0) 10…

A: The given integral is: ∫dx64-10x232 (B) To find: Which integral do you obtain after substituting for…

Q: Find (3x + y)dA where D = {(x, y) | x² + y² ≤ 16, z ≥ 0} Round your answer to four decimal places.

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Q: Compute ₁₁x dx using the concept of integral as limit of sums.

A: The given integral is ∫-11xdx use the properties of integral: ∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx, where…

Q: What is the general solution to the the differential equationy'''=0? A y=C₁+C₁₂x 1 By=C₁+C₁₂x+C₁₂x²…

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Q: Let a = (-5, 1, 2) and 6 = (2, - 1,3). Find the angle between the vector (in radians) Check Answer

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Q: у=ех

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Q: Use the cross product u x v to find the obtuse angle between vectors u and v, where u = i +8j + k…

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Q: 1. Which of the following functions grows the fastest as x goes to infinity? O 2x О 3x O Ox20 ex

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Q: 1. Find the derivatives of each of these functions: a. y = ln (4x² + 4) b. y = 22² c. y = 25x+7…

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Q: Consider the vector whose initial point is P(-6, 1) and terminal point is Q(-5, -3). Find the…

A: We need to find vector.

Q: The regions A, B, C, D, and E in the figure below are bounded by the graph of the function f and the…

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Q: Suppose a company's profits are given by P = x^2 y, where x is the amount of money they spend on TV…

A: given  P = x^2 y x+y=12

Q: Evaluate the definite integral. 1³ sin (4t)dt

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Q: Let f(x) = x^2 - 4x + 1. What is the equation of the tangent line to f(x) at x = 2? Use the limit…

A: Please see the below picture for detailed solution.

Q: Find the following limit. lim

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Q: Evaluate the Integral using the following values. [°x³ dx = 260, [°x dx = 10, [°dx = 2 [°(22-7x-x²)…

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Q: 2. Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives få and fy at the…

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Q: Evaluate [/FO f(x, y, z) ds. f(x, y, z) = xy Z S: z = x² + y², 9 ≤ x² + y² ≤ 81

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Q: xy - Y lim(x,y)→(1,0) (x − 1)² + y²

A: Please see the below picture for detailed solution.

Q: What is the general solution to the the differential equation 3y''-y' - 2y=0? (2/2)

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Q: 5. (y4 - 2xy) dx + 3x² dy = 0; when x = 2, y = 1.

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Q: Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for…

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Q: Given x = y² + y + 1 from 0≤ y ≤2 1. The arc length of the given curve over the interval is 9. 7:38…

A: Given: x=y2+y+1 from 0≤y≤2To Find: To determine the arc length of the given curve over the given…

Q: Solve the differential equation (1 − xy)−²dx + [y² + x²(1 — xy)−²] dy + x²(1 − xy)−²] dy = 0; y (2)…

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Q: Answer: Use a triple integral to find the volume of the solid enclosed by the paraboloids y = x² +…

A: Let's find volume by using triple integral.

Q: J 9(x, y, z) dV over solid B. B = {(x, y, z) | x² + y² ≤ 9², x ≥ 0, y ≥ 0,0 ≤ z ≤ 4} and g(x, y, z)…

A: Please see the below picture for detailed solution.

Q: The function f is shown below. What is the value of answer in simplest form. -10-9-8 5 4 3 2 11 8 6…

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Q: -) 1 = dx x (1-√x)²

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Q: Find a formula for the sum of n terms. Use the formula to find the limit as n Ilm (-1)²

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A: Find the domain and range of the function fx=51-e3x

Q: Write a limit using summations that would equal So 0 tan (2x) dx.

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Q: 2. Solve the differential equation dx for y = f(x) with the initial condition y(0) = 2.

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Q: Differentiate the following function. You do not need to simplify the derivative. F'(x) = F(x) = 6e²

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Q: Find the domain of f(x) = √6x +9

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Q: 12. What transformations are applied to the parent function f(x) = x² to obtain the graph of the…

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Q: 3. Evaluate f(x) = 15 – ½ (x) for f (4). a) 16 b) 14 c) 13 d) none of the above

A: 3.  This is a problem of polynomial.  Here given a polynomial f(x) and find f(4).

Q: 3. Consider the following vectors: ä=7-2] +3k, b=27-3k, and a = -37 +2j. Compute the required…

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Q: so xe x dx

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Q: i) lim cos x-0 7 πCOS²x x²

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