Determine whether F is conservative. If so, find a functionf such that F= Vf. F(x, y) = (16z-24xy le-6oi-24x'e-6j O fr. y)= 4xe-6y +C O not conservative O fr.y)= (48-24x)o-6y +C O fr.y)=(424-4yle-6ry +C

Q: b) following function is defined Determine the point(s) where the g(x, y) =…

A: Given function is: gx,y=-x-34ln4y+6-36x2-36xy-9y2. The function is defined when: gx,y≥0.

Q: 221. y = y = (3x² + 1)³ 223. y = y = ($+7) 772 SHALL NO 225. y = сsс(лx + 1) 227. y = -6sin ³x -3

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Q: Find the domain of the function. Then compute the value of the function at the given point. f(x,…

A: To calculate domain of f(x,y)

Q: Suppose that f(z) = x² - y² - 2y + i(2x - 2xy), where z = x+iy. Write f(z) in terms of 2, and…

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Q: السؤال 12 What is the degree of the differential equation dy d.r3 5x* – 622 ? - 6x² .A .B 5 .C 4 .D…

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Q: 1. Find the following for the function f(x, y) = 3x³y² - 5x + 26y - 9.

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Q: Let f(z) - 4z-1 pnd alz) - ar+b, where a pnd b are positive constants. If the composite

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Q: of and ду of For the function f(x,y) = In (x+ 3y), find

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Q: 3. (b) Consider the function f(x, y) = a(x² + y²) + xy + 1 for some real number a. Find Vf. Find fxx…

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Q: Q7. Check if the following functions are Orthogonal or not? fi(x) = x°, f2(x) = x² + 1 [-1, 1] on…

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Q: 3. Check for monotonicity for the following functions. TR = -20² + 14Q %3D TC = 20 + 10 100 AC = Q +…

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Q: The domain of the following function: is: f(x, y) = Select one: O A. D= {(x,y) y ≤7-3x} O B. D= {(x,…

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Q: Compute fFdr, where F(x, y) = (5+27x², 2xy) and C is a line segment from (0, 0) to (1,2). (Use…

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Q: f(x,y) = x²y + 2xy² + 5y³

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Q: if z=x+jy, then  check whether the function f(z)=1/1+z2 is an entire function .state the reasons

A: According to the given information, it is required to check whether the given function is entire or…

Q: .Let f, g andh are three functions defined as below : f: R>Rf(x) = 4x² – 4, - g. R→R8 (x) = V-5x+…

A: Given  f(x) = 4x2-4g(x) = -5x+1h(x) = 2x-5   a) fog(x) = f(g(x)) = f(-5x+1) = 4-5x+12-4 =…

Q: z) = (x2 + then (a + E

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Q: Find fx and fy for f(x, y) = (1 - 2x + y)ex+2y Select one: a. None of these b. fx = c. fx (2 + x -…

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Q: Find fay (1.2) for f (x, y) = x²In(7 + y) +. 35 19 36 36 19 35 36 36

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Q: Find f(k-1) when f(x) = 5x² + 3x + 6. OA. f(k-1)= -7K² +5k+8 OB. f(k-1)=5k2-7K+8 OC. f(k-1)=5k²-7k+…

A: Given,

Q: Q7. Check if the following functions are Orthogonal or not? fi(x) = x* , f2(x) = x² + 1 (-1, 1] %3D…

A: Two functions, f1 and f2 are said to be orthogonal if <f1,f2>=0 over the common domain of the…

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Q: Find the standard factorization of the entire function f(z) = cosyz

A: Using the Euler's formula as, cosθ+isinθ=eiθcosθ-isinθ=e-iθ Now adding both the equations,…

Q: 2. Let f(x) = 3x + 6 € Z7[x]. Find all associates of f(x).

A: The given function is fx=3x+6∈ℤ7x To find: the associates of f(x).

Q: 2. In each case, write the function f(z) in the form f(z) = u(x, y) + iv(x, y): z² (a) f(z)=z³+z+1;…

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Q: Find real numbers a,b,c,d such that And then find f'(z) =? f(x) = x² + axy + by² +1(cz² + day + y²).

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Q: Differentiate the following functions using product rule. 1. f (æ) = (3x – 9) (x – 6) 2. ƒ (x) = (æ³…

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx

Q: 7. Use the chain rule to differentiate the following functionswith respect to x. (a) y = √√√9 – 4x²…

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Q: The function f is defined by f:xx -2r+5, xeR, 121. Find the function gif the composite function…

A: Use the concept of composite function and factorisation to solve the problem.