Let f(x, y) = x² + 2y² and C be the curve a of the following: (a) [ f(x,y) ds (Setup but do NOT evalu

Q: Let X {1,2, 3} and Y {3,4}. Define f : X → Y as follows: = f(2) = 3 and f(3) = 4. Draw an arrow…

A: We will draw the arrow diagram for function mapping from set A to set B.

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

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Q: Find the linear approximation of the function f (x, y) x² + y² at the point (2,-1, 1)

A: Given function:- fx,y=5x2+y2

Q: 2. For F(x, y, z) = (6xsin y+10x=' )i + (3x² cos y-4ye* −2y²z³)j + (-2y³e² +15x²2²)k, find a…

A: Given Data: Let us consider the given data, Fx,y,z=6x sin y +10xz3i+3x2 cos y -4yeyz-2y2zeyzj…

Q: a. Find a function (f(x,y,z)) such that (F = Vf(x,y,z))? b. Use part (a) to evaluate (F. dr ) along…

A: We have to evaluate the ∫CF.→dr→.

Q: Let f(x, y) = 2x²y³ - 2xy. Locate where the relative extrema and saddle points of f occur, if any.

A: The given problem is to find the relative extrema and saddle points of the given function…

Q: Joshua wants to find the local maxium and minima of the two variable function F(x, y) = x³ +y² – 48…

A: We will find out the required points.

Q: Do the curves ri(t) = (t² + 3, t+1, t² – 5) and rž(s) = (4s, 2s – 2, s + 1) intersect? If so, at whi…

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Q: Now compute [(x − 3y² + 2) ds where C' is the union of the curves C1 and C2. C1 is the line segment…

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Q: Let f (x, y) = e3x-49). Find the equation for the tangent plane to the graph of f at the point…

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Q: The equation of the tangent line to the curve x² + y? = 9, at (7,-18) is 7 y = 18 7 (х — 7) — 18 18…

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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: Two sharpshooters will simultaneously shoot once at a target. Let Xi , i = 1, 2, be marksman i's…

A: Given that, the errors are modelled by X1~N(0,0.5),X2~N(0,1). To solve this problem z table values…

Q: Suppose that f(z, y) = e-2-2y –2z+y Then the maximum is

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Q: Let z = f (x, y) be a function of two variables. Prove thatwhen c1 not equal c2, the level curves…

A: The intersection of 2 curves is obtained when both the curves pass through a common point. This…

Q: Evaluate f (5ydy + 3xydx) C if C is the closed curve determined by the x-axis, the parabola y = x²…

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Q: Calculate the maximum and minimum of the function f (x,y) = xy subject to the condition x2 + y2 = 1

A: To find the optimal solution, we will use Lagrange multiplier method. The Lagrangian function is…

Q: Suppose that f(x, y) = 2x² + 2y¹ − 2xy Then the minimum is

A: Given function: f(x,y)= 2x4+2y4-2xy partially differentiating f w.r.t. x, ∂f∂x= 8x3-2y partially…

Q: Let f(x, y) denote the elevation of boring national park, and suppose britbmw is on a slanted part…

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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: 6. The function f(x, y) = (x², y², xy) is a function of f : C² → C³. Determine whether the function…

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Q: Suppose that f(æ, y) = e-2x² – 3y² + y Then the maximum is

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Q: Let f(x, y) = x2 − 2y and g(x, y) = xey . Show that at any point (x0, y0), the level curve of f…

A: To show that at any point the level curve of f and g intersects perpendicular, it is enough to show…

Q: Let (t)=(-5t2+4,t³-+4,2+³) 7 Find the line (L) tangent to (t) at the point (-1,0,2) L: (x,y,₁2)= +t

A: The given problem is to find the line tangent to the given parametric curve at the given point…

Q: Find the length of the curve r(t) (1,t²,), 0sts1 %3D «3 Ost<1

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Q: If f(x, y)= xe2y +y, evaluate grad f •dr where C is the straight line joining the point (2,0) to the…

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Q: Let r(t) = (-5t³ – 1, t² + 5t³, 3t²). Find the line (L) tangent to (t) at the point (39, -36, 12)

A: r→(t)=⟨−5t3−1,t2+5t3,3t2⟩Find the line (L) tangent to r→(t) at the point (39,−36,12)