Find the exact length of the polar curve. r=0², 0≤0 ≤ 6π

Q: Solve the differential equation by variation of parameters. 1 4 + ex y" + 3y' + 2y = 4

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Q: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

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Q: Evaluate the integral. if -2 ≤x≤0 [₁ f(x) dx where f(x)=4-x² if 0<x≤4 22 x Enhanced Feedback Please…

A: Here we have to find the integral.

Q: A) Let g(x) (5x+24 =x² 2x+8 x<-3 -3<x<4 x 24 a) lim g(x), lim g(x) X--3 evaluate the following…

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 12e* - 12 y(x) =

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Q: Jse polar coordinates to describe the region shown. y -2 -1 1 1 2 Xx

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Q: 5. Use an iterated integral to find the volume of the solid that is bounded above by the plane…

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Q: 2. (x+y) dx + (3x + 3y − 4) dy = 0

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Q: Question 17 V -2 8- 7 16 16 6 5- 4 3 رها را 2 1 -4 -7 1 > V V 2 3 4 5 Find an equation for the graph…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Evaluate the iterated integral. 2y 1²1,²% (10 + 8x² + 6y²) dx d 0 ly

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Q: Sketch the region R of integration and switch the order of integration. 81-x2 LV²²- -10 O -10 f(x,…

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Q: Find the gradient of the function at the given point. Function g(x, y) = ye-x Vg(0, 9) = Point (0,9)…

A: Given function: g(x,y)=ye-x

Q: 3 g-¹(x) = = (Write your inverse function in terms of the independent variable x.) Find the inverse…

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Q: Find curl(F x G) = V x (F x G). F(x, y, z)= i + 7xj + 6yk G(x, y, z) = xi - yj + zk

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Q: A) Let g(x)=x² (5x+24 (2x + 8 a) lim x-1 b) lim X-0 a) lim g(x), lim g(x) x--3 x-0 B) Find the…

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Q: A proton traveling at 34.2° with respect to the direction of a magnetic field of strength 2.27 mT…

A: Given  θ=34.2° B=2.27mT F=9.44×10-17 N

Q: Sketch the region R and evaluate the iterated integral IT x²y² dx dy y 10 8 6 2 y 10 8 00 6 4 2 [[…

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Q: f₁(x) = 9, f₂(x) = cos²(x), f3(x) = sin²(x) linearly dependent linearly independent

A: Here given  functions are.  9. ,Cos2x  , sin2x

Q: Evaluate the double integralfor, f(r, e) dA. Sketch the region R. O π/6 8 O sin(0) cos(8) dr de -5…

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Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: We have verified that x² and x are linearly independent solutions of the following second-order,…

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Q: f(x) = 2x²-4x x²+1

A: Given :fx=2x2-4xx2+1

Q: 49-2 sin(8) = Video Example 4 EXAMPLE 1 SOLUTION Evaluate |v √49-x² x² Let x = 7 sin(e), where -7/2…

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Q: Sketch the region R whose area is given by the iterated integral. To Se *6 *3 7- 6- 5- 4- 3- نيا 2-…

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Q: Find the radius of convergence, R, for the power series ₁ (−1)n. in=. O R = 0 R = 2/1/2 R = ∞ R = 2…

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Q: Determine whether the vector field is conservative. F(x, y) = (7y - x²)i + (7x + y)j conservative…

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Q: elax upx dx

A: ∫1xlnx23dx

Q: Evaluate the integral. (Use C for the constant of integration.) tan (x) cos(x) dx

A: ∫tan8xcos9xdx

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Given solution is y=C1+C2x+C3e4x

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Integrate f Osin-15x+C ○ -sin-¹5x + C 1 dx 1-25x2 - 5 H|K sin ¹5x + C cos ¹5x + C

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Q: Write the sum of the two iterated integrals as a single iterated integral by converting to polar…

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Q: 3. The Downhill Ski Club is organizing a ski trip. Group tickets for the ski trip are priced at $20…

A: Given Price of ticket for first 100 skiers = $20 Discount in the price of ticket for skiers over 100…

Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 4yz²k; (3,…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: Find the general solution of the given second-order differential equation. 3y" + 2y' + y = 0 y(x) =

A: We need to find general solution.

Q: (-3x)² +1 if x # 4 3x + 13 if x = 4 Calculate the following limits. Enter "DNE" if the limit does…

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Q: Decide which of the two given functions is linear and find its equation. 12 3 4 X 0 f(x) 9 14 g(x)…

A: Topic = Functions

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. 8u, y = uv x = UV a(x, y)…

A: Given,            x=uv-8u , y=uvTo find : Find the Jacobian ∂x,y∂u,v for the indicated change of…

Q: Exercise (b) Find the slope of each secant line. Step 1 Recall that the slope of a non-vertical line…

A: Since the secant line is passing through another point Q(3,3) Therefore we will substitute x = 3 in…

Q: dw = t³ and y = 7. Find dt Let w = cos(8x - 10y), where x =

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Q: Determine whether the vector field is conservative. F(x, y) = xe+²2y (2y + xj) conservative O not…

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Q: Suppose 150 trout are seeded into a lake. Absent constraint, their population will grow by 35% a…

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞, 00). f₁(x)…

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Q: Consider the following function. f(x) = x¹/⁹ + 5 (a) Find the critical numbers of f. (Enter your…

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Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson's 3/8 rule with (n₂ = 3) to estimate tan-¹(2).…

A: We have to estimate the given function.

Q: A rocket is fired upward from some initial distance above the ground. Its height (in feet), h, above…

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