Determine whether the vector field is conservative. F(x, y) = 6y6(yi + 7xj) conservative not conservative

Q: Examine the function for relative extrema. f(x, y) = 2x² + 7y² - 4x − 14y + 12 (x, y, z) = ((No…

A: Given function: fx, y=2x2+7y2-4x-14y+12

Q: Use the substitution t = -x to solve the given initial-value problem on the interval (-∞o, 0) x²y" -…

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Q: Given the unit circle, x^2 +y^2=1. Sketch the unit circle and pick a point K(a,b) on the unit circle…

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Q: b y' = 2 + ₁e-ax a

A: details steps are given in step 2

Q: Find the derivative of f(x)=(x2−2x)(3x+5) by first multiplying then simplify.

A: Here we have to use the concept of derivatives

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

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Q: Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector…

A: The given surface is zex^2-y^2-1=0 and point (6,6,1).

Q: A function f is said to have a removable discontinuity at a if: 1. f is either not defined or not…

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Q: Find the general solution of the differential equation y" - 2y + y = 7et 1+t2 NOTE: Use C₁ and C₂ as…

A: Given the differential equation is y''-2y'+y = 7et1+t2

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: This question has several parts that must be completed sequentially. If you skip a part of the…

A: We need to fill in the blanks.

Q: The length of a rectangle is three times its width. If the area of the rectangle is 108 yd², find…

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Q: Solve the following ODES by Undetermined Coeff 11 4X y - 16 y = 19,2 € + 60e, y(a) = Y(u). 4X -4X…

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Q: The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its…

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A: Given that      differential equation   6y''+y'-y = 0      ,        y1= ex3         and…

Q: 2. The function ƒ(x) = x² − 4 is transformed to g(x) =— (x² − 4). Compare the domain, range,…

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Q: 10z +2 (z+1)²(2-3)² S dz

A: ∫10z+2z+12z-32dz

Q: Find the general indefinite integral. (Use C for the constant of integration. Remember to use…

A: simplify the expression and solve the integral

Q: 13) x+2 x+4, Which inequality is equivalent to *-*+4? = x-3 x+1 a. treb. 2x² + 4x-10 (x-3)(x+1)…

A: This is a problem related to linear inequalities. Please follow the procedure given below.

Q: se e differential equation x²y" - 6xy + 10y = 0; x², x³, (0, 00). the given functions form a…

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

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

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Q: Sketch the region R and evaluate the iterated integral -1.0 O [²L²¹²- -0.5 (12x+8y) dy dx y 3 £₁ […

A: We can evaluate the given integral by using the integral formulas.

Q: TT/4 0 tant di

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Q: Find the general solution of the given second-order differential equation. 25y" - 15y' - 4y = 0…

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Q: (2xy - x + 2y - 1) dx + (8x² y² -2x + 4xy² − x) dy = 0 -

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

A: Given solution is y=C1+C2x+C3e4x

Q: Please solve part d)

A: To determine the points on the curve y=tan-1x, where the slope of the tangent line is the curve…

Q: What is the maximum value of the function h(x) = 10x =—= 22² x² on the interval 0≤x≤ 40 and for what…

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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: (-tanx) ydx + Inlexy cos x| dy = 0

A: We need to find out the general solution of the given differential equation.

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

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Q: ƒ(x) = (x³ – 4x) 10

A: Solve the derivative

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

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Q: VALUE INSIDE THE CIRCLE cos² x Yp = D²+1 For given particular integral multiplying and dividing by 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: 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: (x + y) dx + (3x + 3y - 4) dy = 0

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

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Q: Prove the identity. cos(3x) − cos^3 x = − cos x sin^2 x − sin x sin(2x)

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Q: Sketch the region R whose area is given by the iterated integral. L1²5-1² dx dy

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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: Determine whether the given set of functions is linearly independent on the interval (-∞0,00). f₁(x)…

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

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Use the one-to-one property of logarithms to solve. (Enter your answers as a comma-separated list.)…

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Q: Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that…

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Q: Consider the following. u = 2i + 6j v = -7i+j+9k Find u x v. Determine if u x v is orthogonal to…

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Q: Evaluate the triple iterated integral. LLL Jo π/4 6 6-r rz dz dr de

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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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