Compute the flux of the vector field (x², – xy³), out of the rectangle with vertices (0,0), (1,0), (1,6), and (0,6)

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A: The cost function Cx=-19x2+70000x+20613 dollarsThe Revenue function Rx=-24x2+220000x dollars

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Q: 2. (600) A linear second-order differential equation is given as y" + 3y' + 2y = 5e¯* + 10 sinx a)…

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Q: (1) Evaluate the following limit y-r lim (z.y)-(2,2) x² - y²

A: Evaluate the limit  lim(x, y)→(2,2)y-xx2-y2

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A: F→=5zcosx,3zsinx,7z

Q: 7. Find all critical points of the given function and use the second derivative test to identify…

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Q: Evaluate fry³da + zªdy, where C'is the rectangle with vertices (0,0), (2.0), (2,1), and (0,1)…

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Q: Determine interval of convergence of the series (-1)" (4x+1)" O (-1/4, 4) O (-00,00) O (-11, 3) O…

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Q: he = = = du 00 r cos 0 cos oT + r cos sin ój-r sin OF or

A: hθ=|rcosθcosϕi+rcosθsinϕj-rsinθk|

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Q: Find zdy + yda, where C is the arc of the curve y = e* for 0 ≤ x ≤ 2

A: To find ∫Cxdy+ydx  where C is the arc of the curve y=ex for 0≤x≤2

Q: Find [(5x + 4y)dA where D = {(x, y) | a² + y² ≤ 4, x ≥ 0}

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Q: The gradient of f(x, y) = e³-² sin(4 - y) at (x, y) = (1, 3) is defined as followed: ▼ f(x, y) =…

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Q: n Σ (-1)^ n=1 3 V8 tnlo

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Q: Let F = xyi + xyj + xyzk. Find div(F).

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Q: 2. Use cylindrical shell method to find the volume of the solid obtained by rotating the region…

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Q: 4) S2 2x√√x² + 0 +3dx

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Q: Use differentiation and/or integration to express the following function as a power series (centered…

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Q: Evaluate the integral. Check your answer by differentiating. (Remember the constant of integration.)…

A: The integral is ∫34+x10dx

Q: Consider the vector field F = Evaluate r(t) = t²i+t³j, 0 < t < 1 Calculator Check Answer (F F dr…

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Q: Find the volume of the solid bounded below by the plane z = 1 and above by the sphere x² + y² + z² =…

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Q: owing rung f(x)-5-x-81 (a) Find the critical numbers of f. (Enter your answers as a comma-separated…

A: f(x)=5-|x-8| derivate and equate to zero equate to zero No solution at x = 8

Q: Year: Month: Date: Ex:-find the are. How Length x=y² oxy 51 Sa Su Mo

A: Arc length  = ∫y=ay=b 1+dxdy2 dy

Q: The gradient of f(x, y) = e³¹ sin(2 - y) at (x, y) = (2, -3) is defined as followed: - - V f(x, y) =…

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Q: SS₁ F Use the Divergence Theorem to calculate the surface integral F(x, y, z) = (cos(z) + xy²) i +…

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Q: 5. 1.² (1² 0 (x² + 2x) dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1. Describe the following characteristics for the function y = 2tan4x on the interval 0, details…

A: Solving the problem.

Q: 56. Directrix: y = -3

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Q: Use the U-Substitution Method to evaluate the integral (show work)

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Q: Suppose that f(x, y) = D x at which {(x, y) | 2 ≤ x ≤ 4,2 ≤ y ≤ 5}. Y - ✔ Then the double integral…

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Q: з Σ (-1)^ hai боu итиеть n ди

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Q: F-dr along the curve C: Consider the vector field F Evaluate F F(t) = t²i+t³j, 0≤ t ≤ 2 PARKING

A: Change the given integral in terms of 't' .

Q: Find the points (x, y) at which the polar curve 2 cos 0,- horizontal tangent line. Vertical Tangent…

A: To find the points x, y at which the polar curve 2 cosθ,  -π6≤θ≤π3, has a vertical and horizontal…

Q: Evaluate So² Tyds where C is the right half of the circle x² + y² = 4 C

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Q: New folder Canva a Amazon Seller i News View my existing or... If there is no solution, enter '0' in…

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Q: Find the curl of the vector field F = curl F = 2.1 + j+ k

A: We are given a field F=yx2, xz5, zy3, we need to calculate the curl for the given field. This can be…

Q: Find the radius of convergence, R, of the series. R = ∞ Σ 47n²x7 n = 1 Find the interval, I, of…

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Q: Find the center of mass of the solid S bounded by the paraboloid z = 2x² + 2y² and the plane z = 10.…

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Q: The rate of change in z at (1,4) as we change x but hold y fixed is The rate of change in z. at…

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Q: Determine the volume of the solid with base B, bounded by y = √x, y = 0 and x = 4 if the…

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Q: Use Green's Theorem to evaluate [F(r) dr с

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Q: Evaluate fry³da + zªdy, where C' is the rectangle with vertices (0,0), (4,0), (4,2), and (0,2) C…

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Q: C)u= Inx, dv = ln x. dx (5) If x = 5sine,≤0 ≤ C#/2 D)u= x,dv= Then tan 0= A) 11 √25-x² B) √25-x² T…

A: Given that, x=5sinθ , -π2≤θ≤π2⇒sinθ=x5

Q: 3. Consider the vectors [1,2,3] and [-1,4,8]

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Q: 7) [2x²e²* dx

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Q: Let P be the plane in space that intersects the x-axis at 2, the y-axis at -2, and the z-axis at -4.…

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Q: Let z = √x+3y. Then:

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