Let f(x,y) = x2y4sin(1/sqrt(x2+y4) ) when (x,y) =/ (0,0) and f(0,0) = 0 Determine if f is continuous in origo

Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

Q: Value of divergence of function (x2y2)î - (z³y 4x) ĵ + 4y² xk at (1, 2, 1) is

A: Given vector is (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

Q: Bounded by the cylinder x 2 + y 2 = 1 and the planes y= z x =0 z= 0 in the first octant

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Q: Assume the second derivatives of ƒ are continuous throughout the xy-plane and ƒx(0, 0) = ƒy(0, 0) =…

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Q: a) Find the directional derivative of f(x, y, z) = x²yz + 4xz² at (1, -2, 1) in the direction 2i - j…

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Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized? |

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Q: Find f-(x, y) and fy(x, y). f(z, y) = (y° tan(5z)) f-(x, y) fy(x, y) =

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Q: Choose the gradient of the function f defined by f(x,v,z) = cos(xy +9xz + 13yz). O sin(xy O -cos(…

A: Take gradient and solve

Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

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Q: Find the partial derivative f(x,y) = x7y fx(x,y) = ? fy(x,y) = ?

A: The given function is: f(x,y)=x7y

Q: Find the direction 0 in which the directional derivative of the function x + y f(x, y) = 2(x + y) -…

A: Given that: f(x, y)=2(x+y)-x+yxy

Q: : Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² + 2y²…

A: To find the directional derivative of the given function.

Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy² = 2 (C- cos x) O…

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Q: Prove that the function ((z*)2 Iz| > 0 f (z) = z 0, z = 0 is not analytic at z = 0 by calculating…

A: Given function is f(z)=z*2z, z>00,        z=0 we have to prove, the above function is not…

Q: Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (1, – 1) and…

A: We have to find the directional derivative of the given function in the given direction and at the…

Q: What is the linearization L(x, y) of a function f (x, y) at a point (a, b)? How is L(x, y) connected…

A: Linearization L(x,y) of a function f(x,y) is given by the formula

Q: . Find the directional derivative of y fx, у, 2) x+ z at P(2, 1, – 1) in the direction from P to…

A: NOTE: Refresh your page if you can't see any equations. . the given direction is P to Q find the…

Q: Let f(x, y,z) = z-sin(xy), x t, y Int, z et1. Find derivative of f directly and by using chain rule…

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Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized?

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Q: Show that the function x² – y² 2ху f(x,y) = { x² + y² if (x,y)# 0 if (x,y) = 0 is continuous at…

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Q: x+y are functions of t.Ue %3D Ronphicit differentiation to express in terms af dx X and y dy

A: Explanation of the solution is given below....

Q: Show that the function defined by xy √x²+y² f(x, y) {{ = 0 if (x, y) = (0,0) is not differentiable…

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Q: Let f(x, y, z) = x In y - exz.Calculate the directional derivative of fat point (-5, 1, -2) and…

A: In this question, we find the directional derivative of the function f(x,y,z)=xln(y)-exz3The line…

Q: Suppose that f(æ, y) f(x, y) in the directional (1, – 1) and at the point = xy. The directional…

A: Here, the given function is: f(x,y)=xy So, ∇f=∂f∂x,∂f∂y⇒∇f=y,x⇒∇f(4,-3)=-3,4

Q: The gradient of f(x, y) = e³ ² sin(3 - y) at (x, y) = ( - 1, – 3) is defined as followed: V f(а, у)…

A: It is gradient vector by using partial derivative

Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy²= 2 (C- cos x) O y…

A: This question is related to differential equations, we will solve it using given information.

Q: Prove that if the function f : I → R has a bounded derivative on I, then f is uniformly continuous…

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Q: I. Show that the function ƒ defined by (1, y) = (1, –1) f(1, v) = { +g (z, y) # (1, –1) + y is not…

A: We will use the sequential characterization of continuity to solve this problem. The detailed…

Q: Plot the function f(x, y) = x² – y² over the square region bounded by the lines y =x - 2, y =x+ 2, y…

A: Given the function fx,y=x2-y2

Q: sin(x+y) x+y (x.y) (0,0) F(x, y)={ 21 (x.y) (0.0)

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Q: Find the directional derivative of f(x, y, z) = xy²z³ at P(3, 1, 1) in the direction of Q(0, -5, 7).…

A: Given function: fx,y,z=xy2z3

Q: Show that the function f(z) = sin x cosh y + i cos x sinh y is continuous as well as analytic every…

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Q: Assume the second derivatives of ƒ are continuous throughout the xy-plane and ƒx(0, 0) = ƒy(0, 0) =…

A: Consider the provided information, fxx0,0=5,fyy0,0=3  and fxy0,0=-4 The Second Derivative Test to…

Q: Find the rate of change of f (x, y, z) = 3xyz in the direction normal to the surface yx² + xy² + yz²…

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Q: I. Show that the function f defined by (r, y) = (1, –1) f(r.y) 2 + y (x, y) # (1, -1) is not…

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Q: Differentiate the function. y = In(In x) y' = %3D

A: Given y=ln(ln x)             y=ln(ln x).y'=ddx(ln (ln x))y'=1ln(x) . ddx(ln x)y'=1ln(x) . 1xy'=1x .…

Q: Find volume y=3x^2, x=1, and y=0 about x axis

A: y=3x^2, x=1, and y=0 about x axis

Q: The maximum directional derivative of f (x, y, z) = x² sin(zy) – yx + 10 | at (-1, 2, 0) is

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Q: Determine f„ (0, T, 1), fy(0, , 1), f¿(0, r, 1) given the function z sin(3xz+ y²)

A: The given function,        zsin3xz+y2

Q: Find the directional derivative of f(x, y, z) = xy²z³ at P(4, 1, 1) in the direction of Q(0, –7, 9).…

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Q: Assume the second derivatives of ƒ are continuous throughout the xy-plane and ƒx(0, 0) = ƒy(0, 0) =…

A: Maxima or minima: Let f(x, y) is any function. 1) Evaluate fxx, y=0 and fy0,0 for critical point. 2)…

Q: If z = f(x,y) = 3x^2 - xy , get the total differentiation of z if (x,y) change from (2,3) to (2.5 ,…

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Q: Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every…

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Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: See the attachment

Q: Assume the second derivatives of ƒ are continuous throughout the xy-plane and ƒx(0, 0) = ƒy(0, 0) =…

A: Given that, ƒxx(0, 0) = -6  ƒyy(0, 0) = -3 ƒxy(0, 0) = 4

Q: /alue of divergence of function (x2y2)î - (z³y – 4x) ĵ + 4y2 xk at (1, 2, 1) is

A: Let f = (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

Q: If (x, y, z) = cos(x – y)+ e² compute directional derivative of Í at (3, 3, 0) in the direction of ŷ…

A: Option C is correct option.