1)Use Lagrange multipliers to find the extreme values of the function f: R? → R, f(1,y) = 1² – y² subject to restriction r2 + y? = 1.

Q: Let P denote the path that travels along the graph of y = x2 from (0,0) to (1,1). Let f(x,y) = √1 +…

A: Let P denote the path that travels along with the graph of y=x2 from (0, 0) to (1, 1). Let f(x,…

Q: 3. Find the fixed point(s) of f : [1, 0) → [2, 0) defined by f(x) = vx² + x.

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Q: 2) Use Green's Theorem to compute f F df where F= (3x +4y)i + 2xyj and C is the triangular path from…

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Q: Finding the point that is closest to the point (2, 1,-1) among the points in the plane given by x +…

A: We have to find a function of two variables such that when we minimize it, we will obtain a point…

Q: 8, find the the function maximum value of +(x, y,Z) 2179`x+ 2y -12+7 subJect to Constrain t+3 +2² =…

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Q: 1. For the function f(x, y) =√x²-y-1 a) Find and graph the domain of the following function. b) Make…

A: (a)  Domain of f(x, y)  is  (see the denominator)          and   Domain of f contains those points…

Q: 3. Let f: R³ R be defined by f(x, y, z) =|| x ||. Find Vf(x, y, z). What is the domain of Vf?

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Q: Describe the domain of the function f(x, y)= In(6+x-y). {(x, y): y<x-6} {(x, y): y 2 0} a. {(x, y):…

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Q: 3. Show that f(x, y, z) fxx + fyy+fzz = 0. = 1 x² + y² + z² satisfies the equation

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Q: If f(z) = z² − (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

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Q: 2. Evaluate [ F C F = (xz, 0, yz) and the path C is the line segment from point (-1,2,0) to (3,0,1)…

A: Given that, Now,

Q: The given functions are concave or convex or neither in the domain: 1). f(x, y) = 2r-y-r²+2ry-y² 2).…

A: As per the question we are given two multivariate quadratic equations : f(x,y) = 2x - y - x2 + 2xy…

Q: - Consider the function f(x) = 2x² - 16x 5 on the interval [2, 6]. Find the value(s) for c that…

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Q: Consider the function ƒ (x, y, z) = 2x² + 5y² + z². a) If ƒ (x, y, z) is the profit made from…

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Q: Find the direction in which the given function is increasing most rapidly at the point P, (-2, –1,…

A: Given function f(x, y, z) = x√(y² + z²) We have find the direction in which the given function is…

Q: 3. If z = f(x, y) with the relation xy²z³ + x³y?z +1 = x + y+ z. Find dz at (1, 1, 1).

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Q: Find the absolute maximum and minimum values of f on the set D where f(x, y) = x² + 4y² − 2x − 8y +…

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Q: Suppose that a = xdy is a 1 form and Y(v1, v2, v3) = ((v1 – v3)² (v2 – v3)²) ædy what is "a ?

A: Given α=xdy-----(i)γ(v1,v2,v3)=((v1-v3)2,(v2-v3)2)---(ii) To find γ*α------(iii) from (ii) we…

Q: A function is defined as f(x,y) = 25xy + 3x³ - 7x² sin(y) aj ay a2f (ii) Find and 1325 3²x (iii)…

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Q: b) Let f: D→ C be a function and Y a subset of C. Show that f¹ [C-Y] =D-f¹ [Y].

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Q: 1. Find the following for the function f(x, y) = 3x³y² - 5x + 26y - 9. a. f(1,2)= b. fy(x, y) = c.…

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Q: Let f: R2 R2 be the function given by f(x, y) = (x + y, y). Prove or →>> 8. disprove: f is…

A: Function which is one to one

Q: Two vectors have the following magnitude, A = 11.7 m and B = 10.7 m. Their vector product is:  A⨯B…

A: Given: A=11.7 m and B=10.7 m. And A×B=-1.5 m i+11.3 m k

Q: For the function f(x,y) = 6 of find and 8x+3y' dx dy

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Q: 3. Determine whether each of the following functions is a bijection and explain why. (a) f: R R,…

A: Note:As our company  guidelines we are supposed to answer only first 3 sub-parts. kindly re-post…

Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: 2. Let f= L(X,Y). Show that ƒ is one to one iff (f(x).(x)....(x)) is linear independent when (x,x)…

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Q: 2. Let us define a. Verify that f(x, y) = c. Now consider the function git Similarly, consider the…

A: Given Data: Let us consider the given function is fx,y=xyx2-y2x2+y2

Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

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Q: Show that f : ℝ → ℝ, f(x) = 5x − 3 is a bijective function.

A: The given function is f:ℝ→ℝ defined by fx=5x-3. We say that a function f is bijective if it is both…

Q: The range of the function f(x, y) = 6 – /4 – 2² – y?is O [4, 6] O [4, 0) 0 (-0, 4] 0(-0, 6| O (6,…

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Q: h. By completing the square, re-express fx,y (x, y) in the form fx,y(x, y) = e-(ax-by)² e-cy², Where…

A: Suppose X and Y are jointly distributed with pdf  where .