Consider the function f(x, y) = (a) Find f(0, 0) and f(0, 0) fx(0, 0) fy(o, 0)= (b) Determine the points (if any) at which f(x, y) or fy(x, y) fails to exist f(x, y) and f(x, y) fail to exist for y -x1/5, x 0. O f(x, y) and f(x, y) always exist. Of(x, y) and fx, y) fail to exist for y x, x # 0 f(x, y) and f(x, y) fail to exist for y x1/5, x * 0. f(x, y) and f (x, y) fail to exist for y 0. -x, x

Q: (a) Find the points (x ,y, z) in space, where the function f(x, y, z) = Vx² +y -1 Is continuous.

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Q: (xy(x²-y²) Let f(x, y) =} (x²+y²) (x, y) ± (0,0)| show that fxy (0,0) + f yx(0,0) (x, y) = (0,0)

A: This question is taken from the partial derivative in which we have to prove the given statement. We…

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Q: Given f(x,y)=3.xy² -2y+5x²y° . (i) Compute the first order derivatives f, (x, y) and f,(x,y)· (ii)…

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Q: Exercise 4. Show that the function f is not differentiable at (0,0) f(x, y) = x³ + y³

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Q: Consider F and C below. F(x, y, z) = yzexzi + exzj + xyexzk,   C:r(t) = (t2 + 1)i + (t2 − 1)j + (t2…

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Q: II. Let f(x,y) = (x³ – y², x² y). Obtain a linear approximation of f(x, y) at the point(-1,1) and…

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Q: Find div F if F(x, y, z) = (x² + y)i + z²j + (eY - z) k.

A: Our Aim is to find the value of div F if F(x,y,z)=x2+y i +z2 j+ey-zk -(i)Let  F(x,y,z)=x2+y i +z2…

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A: f(x,y)= 2x-7y+3 fx  = 2 fy = -7 The linearization of a function f(x,y) at (a,b) is given by L(x,y) =…

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Q: Find the linearization of the function f(x, y, z) = xy+ yz + zx at the point (1,1,1).

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