Consider the function. f(x, y) = 5(y + 1)x² Identify the point(s) on the graph of f at which the tangent plane is horizontal. O (x, 0) for only x > 0 O (x, 0) for all x O (0, 5) O (0, y) for all y O (5,0)

Q: xy Prove that the function f(x, y) is differentiable everywhere in its do- x² + y? main.

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Q: 3. find the derivative of the function at Po in the direction of u. f (x, y,z) = 3e* cos yz,…

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Q: Find the derivative of the function at Po in the direction of A. h(x, y, z) = cos xy + e + In zx,…

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Q: Find the linearization L(X,Y) of the function  f(x,y)=y-1/x+1 at(0,0).

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Q: 7. Determine which of the following functions are differentiable at all the z-plane or some region…

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Q: 2. Consider the function of two variables f(r, y) defined by parts as ² + y? f(r, y) = { 2/r² + y² +…

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Q: 2 The tangent plane to the graph of the function ƒ : R² → R defined by f(x, y) = −1+ cos(xy) +…

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Q: Find the direction at which the function f(x, y, z) increases fastest at (2, 0, 0) = x In(e' – xz)…

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Q: that f(4, 1) A differentiable function f(x, y) has the equation of the tangent plane at the point on…

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Q: ib Show that the function defined by F(x, y) xy √² + y² O is not differentiable at point (0,0) if…

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Q: 3. Given the function f(x, y, z) = In(x² + y² – 42²), find the directional derivative f, in the…

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Q: Find the direction in which the function is increasing most rapidly at the point P 0. f(x, y, z) =…

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Q: ) Find the linearization L(x, y) of the function f(x, y) = ez+y at (0,0). Use it to estimate f(0.01,…

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Q: Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1…

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Q: 6. Let f(x, y, z) = e¬ª cosh y + z and P: (-1,0, 0). Find the derivative of f at the point P in the…

A: Given: f(x,y,z)= e-xcoshy+z.

Q: xY (a) Prove that the function f(x,y) is differentiable everywhere in its do- x² + y? main.

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Q: xy2 Let f(x, y) = {x² + y+ 0, (x, y) = (0, 0) (x, y) = (0, 0). Show that f,(0, 0) and f,(0, 0)…

A: answer

Q: Let f (x,y)=x2+5xy−4y2. Then a standard equation for the tangent plane to the graph of f at the…

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Q: Using the formula f(x+th)-f(x) t f'(x)= lim: h→0 and admitting the existence of the derivatives of…

A: a) f:R3→R2 defined by fx,y,z=x2+y , x+y+z2 also given z=1,1,2 , h1,1,2 using the formula…

Q: Q4: Find f for f(x,y,z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

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Q: Use the function to show that f(0, 0) and f(0, 0) both exist, but that f is not differentiable at…

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Q: |(y) + (0,0) (x. y) (0,0) Show that the function f (x, y). is continuous at the origin however =…

A: consider the equation  f(x,y)=∑xyx2-y2x2+y2 ,0  x,y  #(0,0)xyx2+y2 where f(0,0)

Q: Consider a function of 3 variables h (x, y, z2) = -3 (2+ Calculate the value of its third order…

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Q: Solve this attachment.

A: Given:fx,y=xy2-x2-y

Q: 3. Let f(x, y) = xy² + x°y². Find an equation for the tangent plane at (x, y) (-1,2). %3D

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Q: Consider the function f(x,y) = [x² + y² if x # (0,0) if x = (0,0) 0 Evaluate f(x, y) over the…

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Q: 2. Use suitable linearization to find the approximate value for the function at point P. f(x,y) (x-…

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Q: 5. Let u(x) be a differentiable function with u(1) = 2 and u'(1) = 3. Find an %3D equation of the…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 3 ex cos (yz),…

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Q: xy -(x,y) (0,0) Let f(x.y) = x +y (0,(x,y)%3D(0,0) Determine whether f(x, y) differentiable at (0,0)…

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Q: Find the derivative of the function at P,(0,0,0) in the direction of B. f(x, y,z) = 3e* cos yz,…

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Q: Using the formula f'(x) = lim h→0 f(x + th)-f(x) t and admitting the existence of the derivatives of…

A: Introduction: In three dimensional Euclidean space, the addition and multiplication of two vectors…

Q: Find the derivative of the function at Po in the direction of A. f(x, y, z) = xy + yz + zx, Po(1,…

A: Given query is to find direction derivative.

Q: (2) Find an equation for the tangent plane to the graph of z = where z = f(x, y) is implicitly…

A: Given: The function is fx,y,z=xy+xz+yz-lnz2+1-4. Calculation: Obtain thethe value of  fxx,y, fyx,y…

Q: (#10) The implicit derivative formula on a surface F (x,y, z) = 0 is: az Fr F, Evaluate dz/ax on the…

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Q: Find the direction in which the function f (x, y, z) = xy - In z is increasing most rapidly at the…

A: We will use directional derivative here