(9) Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = Vf. I F(x, y) = (cos x+sin y+y sec² ry-2x+y²-2xy², 2y+2xy-2x²y+r sec² ry+r cos y)

Q: ey+y°.

A:

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A: Given, r'(1)=<-3,0,4> T'(1)=<2,2,1>

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A: We will use the basic knowledge of vector calculus and differential calculus to answer all three…

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A: Direction derivatives at (1,1) is given in direction of A = 3i - 2j.

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = tan(4x + 5y+z) . F(x, y, z) =

A: given  f(x,y,z)=tan(4x+5y+z)we know that formula of gradient field is→gradient…

Q: Sketch the following vector fields (a) F(x, y) = 2i+xj (b) F(x, y) = 2xi + 4yj (c) F(x, y) = Vf…

A:

Q: . Let n 2 3 be an odd number and f(a, y) = (x" + y")'/n. (a) Determine if f(x, y) is differentiable…

A: We will only use the basic knowledge of the differentiability of functions of two variables to…

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A: Disclaimer: There are two questions here and as per Bartleby policy, I am solving only the first…

Q: One of the following vector functions is a gradient Select one: O (xy? + 2y?)7+ (2y³ – x²y+ 2x)j O…

A:

Q: 3- Complet X f(x) the following table: 0.0.5. - J 2.71828 1.75 5.75460

A:

Q: Let f(x, y, z) = x²y - xy² + z³, P(1,1,2), u is the vector from P to Q(1, -2,-2). Determine the…

A: The given problem is to determine the maximum and minimum directional derivative of the given…

Q: Let r(t)= Determine the interval(s) on which this vector valued function is continuous.

A:

Q: 1. Obtain the directional derivative of: a.. f(x,y) = x²-4x³y² at the point (1,-2) in the direction…

A: Step 1:

Q: 7. For the vector-valued function √t-1 ln(2t - 1) t² - 1 r(t) = (VI- t-1 2 COS πt rt), (t (t = 1):…

A: Let us solve above problem

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = x²y³z¹. F(x, y, z) =

A:

Q: 3. Let f: R2 → R be the function which satisfies for all (x, y) E R² that f(x, y) = 100 – x² – 2y?…

A: A scalar function f(x,y) is a rule that is used to associate a number, or quantity with a particular…

Q: 31. Ke [<cos (1₂) c² - 3+₁ ²+/=/=) +‡ -1 (-1,19,-27, t = 11. Ŕ(t) (1) show that I is continuous at t…

A: This is a problem of vector calculus.

Q: A force field (in newtons) is defined by F(x, y) = [ + + x, 1 x² +1 y³ зав where coordinates x and y…

A:

Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

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A:

Q: Consider the vector-valued function r(t) = cos ti + sin tj + ln(cos t)k. (a) Find the vectors T, N,…

A:

Q: Consider the conservative force field F = (18x²y+9-y)i + x(6x² - 1)j. Find a function f(x,y) such…

A:

Q: ar function = (1, 1, 2) i

A:

Q: 2. (a) Prove that the function f(x, y) = xy is differentiable everywhere in its do- %3D x² + y?…

A: TO solve the question, we use the following facts (a) A functions is differentiable at a point if…

Q: Q1. Find the vector function r(t) given that r(0)= i+2j. and r'(t)= (2et, 3t², 4 cost)

A: The given data is: r0=i+2jr't=2et, 3t2, 4cost Find the vector function rt

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A: As per bartleby guideline for more than one question asked only first is to be answered please…