Use e – 6 definition and show that the function 4x² – y? if (r, y) # (1, –2) 2r + y f (r, y) = • 4, if (r, y) = (1, –2). is continuous at the point (1, –2).

Q: Evaluate the function shown, where ƒ is continuous on [3, 8], ƒ(3) = 4,and ƒ(8) = 20.

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Q: Calculate the linearization L of f(x) : 5e* at x = 1. x2 Express your answer in terms of e and x.

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Q: Consider the function 2+2+z9-2ry+y if (r,y) # (0,0) f(1, y) = if (1, y) = (0,0). (a). Find and at…

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Q: Find the linearization of f(x) = (1+ x)20 at x = 0. Use it to approximate (1.001)20.

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Q: The function f (x, y) = sin(xy)/xy is defined for xy ≠ 0.(a) Is it possible to extend the domain of…

A: conditions of function to be continuous: At each joining point the value of limit from both sides…

Q: For the function f(x,y,z) = In (10x + 7y + 6z), find fy, fy, and f,.

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Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

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Q: Find the linearization L(x,y) of the function f(x,y) = x2 - 4xy + 5 at Po(5,4).

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Q: on f(x, y) = 3x + 9y subject to th %3D

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Q: Find the linearization of f(x, y) = V1+x - y? at (4, 1), and then use it o approximate f(3.96,…

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

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Q: What is the Laplacian of the following function? f(x,y,z)= x² - y² +z?

A: Given function is f(x,y,z)=x^2 -y^2 +z^2. We have to find Laplacian of the function f(x,y,z) .

Q: For the function f(x,y,z) = In (5x + 7y + 1Oz), find f,, f, and f,.

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Q: Consider the following function of two variables: xy g(x, y) = x² + y? Prove that the above function…

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

Q: given that z is a function of x and y which satisfies xyz+exyz=2, find ∂z/∂y using implicit…

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Q: Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c € R. %3D

A: Let us assume that: g(x)=sin(x)and h(x)=(x2+3x+1)So,…

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: \+etari), find f.. S, and f.- xyz 3. If f(x,y,z)= hn 2

A: We have to find fx , fy , fz.

Q: Let f(x) = V17 – x. Compute f'(8) using the limit - definition f'(8) = | 8 Find an equation of the…

A: To find the derivative of f(x)=(17-x)1/2 using limit definition and also obtain the equation of…

Q: For what value of b is

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Q: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

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Q: Find the linearization L(x) of f(x) = cot(x) at x = π/4.

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

Q: For the function f(x, y) = (cos x)ey +v 1 + x + y. %3D Show the process of using the linearization…

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Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: Consider the function 23 – 3y if (x, y) # (0,0), f (x, y) = x² + y? if (x, y) = (0,0). Show that…

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Q: If f =x-e" and F=x'yi-2y'zj + xy'z'k, find: div(F x grad(yf )) at (4,1,-2)

A: The function                     Then, we have to find

Q: Let f(x, y) = ln (3x + y2). Show that fxy = fyx

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Q: 1. Find grad f for the given function below. Ax, y, z) = 5xy + 3yz – 4zx

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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: Find the linearization L(x) of the function at a. f(x) = sin(x), a 6

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Q: Suppose f: a,b] → R is continuous and faf=/ for all xie [a,bl Show that f(x)= 0 ft rEla,b).

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Q: Consider the following function: f(x, y) = {xy cosy/3x2 + y2     if (x, y) 6 not equally to (0, 0)…

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Q: Q10. Expand f (x, y) = e" cosx about up to third degree terms by using Taylor's theorem for a…

A: The given problem is to find the third degree taylor polynomial of given function f(x,y) about point…

Q: Find the linearization L(x) of f(x) = cot x at x = 4

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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: Q3) For what values of a and b are ax + 2b , y = {x? + 3a -b, (3x-5 , 0 2 Continuous at every x ?

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Q: Suppose that f(x, y) = e¯4z² - ly + 7z + 2y then find the discriminant of f.

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Q: Q1. (a) Find the points (x ,y, z) in space, where the function f(x, y,z) = /x² +y² -1 Is continuous.

A: Given :- The points x,y,z in space , where the function f x,y,z = x2 +y2 -1 is continuous.

Q: - Given f(x, y, z) = x In(yz³), find fzy and fyz.

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Q: Find the linearization L(x) of the function at a. f(x)= sin(x), a= π\4

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Q: Find all functions f(x, y, z) such that grad f = 2xi + zj + yk.

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Q: Is the given function f (x, y, z) = xª – 6xy? + 723 continuous at the origin? Yes No

A: If a function f and another function g is continuous at arbitrary point. Then there sum, difference…

Q: Consider the function z = f(x,y). If fx(a,b) and fy (a, b) both exist, and they are equal, then the…

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Q: Q3: Find fxx of the function f (x, y, z) = -In/1-x2 - y2 – z2 %3D

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Q: Suppose w is a function of x, y, and z, which are each functions of t. Explain how to find dw/dt.

A: Given data:"w" is a function of (x,y,z). Therefore, w(x,y,z). And the function x, y and z are the…

Q: if (x, y) # (0,0) (1 if (x,y) (0,0) x+y (a) Prove that the function f(x, y) =2x+y is not continuous…

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