Suppose z is implicitly defined as a function of x, y, by means of the equation: z4+8zx=3x2+12y2 The value of the real constant k for the equality: y*(∂z/∂x)−kx*(∂z/∂y) =−2zy/(z3+2x) is true, corresponds to:

Q: Suppose that f(x, y) = at which %3D - {(x, y) | 3 < x < 4, 3 < y < 5}.

A: we have ,  f(x,y)=xy at which (x,y)|3≤x≤4,3≤y≤5 we have to calculate,  ∫∫Df(x,y)dxdy

Q: 5. Show that the function h(x, y) defined by if r2 + y? 1 is discontinuous.

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Q: If the equation xy+xz3-234yz=0 defines z implicitly as a function of x and y, then the value of az…

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Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

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Q: 5. Show that the function h(r, y) defined by if + y 1 is discontinuous.

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Q: Let f(x)= x2 − 6. Prove that the root of this function is equal to √6 {correct to 2 dp}, and lays…

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Q: The function f(x,y) =26-2x²-y² is continuous at point (2, -3). .A True .B False

A: The objective is to determine whether the statement, " The function fx,y=26-2x2-y2 is continuous at…

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: Find the linear approximation of the function at the given point. f(x y) = 4x²y3 at (-9,7) O A. L(x,…

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Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

Q: Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by…

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Q: Prove that f(x) = [[sin²(2log r)– 3 sin ( 2logt)+2] dt %D 1. Cannot be decreasing any where,

A: To prove that f(x) can not be decreasing anywhere, where f(x) is defined as…

Q: Suppose that z = f(x, y) is implicitly defined as a function of x and y. Determine for 4x²z³ - 5yz²…

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Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

A: The function is given by f(x) =-2x3+6x2-3 To evaluate : The point of local maxima or local minima.

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

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Q: Suppose that f(x, y) = yvx* + 1 on the domain D = {(x, y) | 0 < y < x < 5}.

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Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: Assume that f(r, y) is a function given by if (r, y) # (0,0), f(r, y) = 0 if (r, y) = (0, 0).

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Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given  f(x,y)=x2y

Q: The line tangent to y = ƒ1x2 at x = 3 is y = 4x - 10 and the line tangent to y = g1x2 at x = 5 is y…

A: The line tangent to y=fx at x=3 is y=4x-10 and the line tangent to y=gx at x=5 is y=6x-27. Consider,…

Q: Suppose that F(t) is a twice-differentiable function of one variable. Define the function f(x,y) =…

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Q: The function y== In (3z - 2) satisfies the IVP: (3z – 2)°y" + 9 = 0, y(1) = 0, y'(1) = 8. Select one…

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

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Q: let s(t)=3sin(2t)+5. find the absolute maximum and minimum of the function on the interval [0,2pi]

A: We have to find

Q: B)Is w = Zez analytical function or not?

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Q: Let f(x, y) = − sin2 (2x − y) Evaluate fx and fy at (π / 4, π / 3)

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Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

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Q: Find a and b so that the function S4z - 3x² + 4, z -2 is both continuous and differentiable. a = b =

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Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: Verify that Rolle's Theorem can be applied to the function f (z) =2³ – 10z2 +27z – 18 on the…

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Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

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Q: Suppose that f(x,y,z)=x^2yz−xyz^3 is a function of three variables.

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

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Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

Q: Find the values of k in f(x)=x^2-kx such that the line y=5x-4 is tangent to the function.

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Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

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Q: 16. Determine if 4x – 3xy + yʻ is homogeneous or not. If it is homogeneous, state the degree of the…

A: Given : f(x,y)=4x2-3xy+y2   To Check : f(x,y) is homogenous or not and it's degree, if it is…

Q: Verify that Rolle's Theorem can be applied to the function f (z) = 23 – 10z2 +27x – 18 on the…

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Q: Find all points (x.y) where f(x.y) has a possible relative maximum or minimum. Then use the second…

A: Given f(x,y)=x3-y2-48x+8y

Q: Q1) check the continuity of fX) at X--1, 0,1.2,3 -1<x<1 f(x) = 2x-1, 3x-2 2SxS3 2, 1=3

A: As per the answering guidelines we need to answer only first question so please repost the other…

Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x−1, [2,…

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Q: 2. Consider the function а(т — 2) Vx +2 – 2 - if x 2, 2x 2 x² - where a, b, c are real numbers.…

A: Given function is  f(x)=a(x-2)x+2-2   if x&lt;2b                     if x=21x-2-cx2-2x  if x&gt;2…

Q: Suppose that f(x)=xu(x), where u(x) is a differentiable function at x=2 such that u(2)=3, u'(2)=1.…

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x3, [−4,…

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Q: Suppose that a function f(x, y) satisfies fxx fyy – (fxy)² > 0 at a point (a, b). How is the sign of…

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Q: If f(z) is analytic with constant modulus show that f(z) is constant u=3x²y+2x²-y³-2y²

A: To Proof :-  If f  z is analytic with constant modulus , show that f  z is constant.  Given :-  The…