Sketch f(x,y) = x/y contour map, and draw cross-section x=2 to y=2

Q: Find the gradient of the function f(x,y) = 4y - 9x at the point (9,3). Then sketch the gradient and…

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Q: Find the between the two curves. area 2. X=ay, a'y=x 3

A: The area between the curves can be calculated by integration. The formula used for the integration…

Q: Calculate the gradient. f (x, y) = cos(x^2 + y)

A: Calculate the gradient. f (x, y) = cos(x^2 + y).

Q: At what points (x, y) in the plane are the functions continuous? g(x, y) = 1/(x2 - y)

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Q: The equation of tangent plane to the surface f(x,y, z) x+ y +z-9 0 at the point (1,2,4) is x+y+z=…

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Q: Find equations for the tangent plane and the normal line at point Po (Xo.Yo.Zo) (5,2,0) on the…

A: The equation of the surface is -cosπx+2x2y+4exz+4yz=105. The function is fx, y,…

Q: The tangent plane to the surface with equation at the point where (x, y) = (1,0) has the equation z…

A: According to guidelines I solve the first question only.So kindly request you to repost the…

Q: Given a surface f(x,y) = 0x + (4)y. Find the derivative in the direction of v = at the point (6,…

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Q: Find a gradient of the equation: F(x,y) = v2x + :- y sin a + 4 VF =?

A: Here, the given vector equation is: F(x,y)=2x+xy-y2sin x+4

Q: Use the Chain Rule to find at aw w = x² + y² + z²; x = 10tsin s, y = 10tcos s, z = 9st² əs Find the…

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Q: Let f(x, y) = x2 – y?. Find (a) The directional derivative of f at (-2, 1) in the direction of v = i…

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Q: The gradient of f(x, y) = zy at (z, y) = ( – 2, – 1) is %3D

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Q: Find the gradient of the function f(x,y) = /4x+2y at the point (- 1,4). Then sketch the gradient…

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Q: If the gradient of f is Vƒ = z j - yi – 2xzk and the poi f(x, y, z) = 0, find an equation for the…

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Q: Find the moment of inertia of the area of the loop y2=x2(1-x), with respect to y-axis

A: We have to find the moment of inertia of the area of the loop y2=x2(1-x), with respect to y-axis.

Q: 5. Find the linear approximation (i.e. the tangent plane) of f(x, y) = Vx/y at the point (9, 4) and…

A: The Local Linear approximation of f at (x,y) using the partial derivative f at (x0,y0) is given by…

Q: Find the gradient of the function f(x,y) = 5y - x at the point (9,1). Then sketch the gradient and…

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Q: Given a surface f(x,y) = -2x² + (-3)y“. Find the derivative in the direction of v = at the point…

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Q: How will the contour maps of f (x, y) = x and g(x, y) = 2x with contour interval 1 look different?

A: To describe how the contour maps of f(x, y) = x and g(x, y) = 2x with contour interval 1 look…

Q: Find the equation for the tangent plane and the normal line at the point Po(3,3,1) on the surface x…

A: To find an equation for the tangent plane and the normal line at the point (3,3,1).

Q: The directional derivative of f(, y) = In(x² + y²) at the point P(1,5) in the direction v (3, 4) is…

A: We have to find the directional derivative of the function fx, y=lnx2+y2 at the point 1, 5 in the…

Q: Line WY bisects Line UV at Y. If UY = 2x + 1 and YV = x +7, find UV.

A: Meaning of biscsts is dividing into 2 parts .

Q: Given a surface f(x,y) = -2x² + (5)y². Find the derivative in the direction of v = at the point (7,…

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Q: Let r(t) = (cost,sin t, ln(cost)).Find T, N, and B at (1, 0, 0).

A: Let rt=cos t, sin t, lncos t at 1,0,0 Find T, N and B. Tangent vector to the curve is denoted by…

Q: Find the gradient of the function f(x,y,z)=2xe^(y/3)sin(3z). grad f=

A: Given f(x,y,z)=2xe(y/3)sin(3z) We need to find gradient of f(x,y,z)

Q: Find the maximum rate of change of fat the given point and the direction in which it occurs f(x, y)…

A: The maximum rate of change of given f(x,y) at point (4,9) is,

Q: Find the gradient for the function f(x, y) = x5 sin(xy) at the point (, 10) Find exact values. No…

A: To find the gradient of a function (which is a vector), differentiate the function with respect to…

Q: Find an Equation for the tangent plane and normal line at the points Po on the given surface. x +…

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Q: Test for an extremal of the functional F[y(x)] = |,´(y'² - y?)dx, y(0) = 0, y = 1 2 0,

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Q: A/Find the distance between the line 2x + 3y = 5 and the point(-1,0). ( B/Find by integrating along…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Fx to find dy Assuming - 7x - 9y2 - 2xy = 0 defines y as a differentiable function of x, use the…

A: To find the derivative using the theorem

Q: Find the gradient of the functions below. a)f (x, y, z) = sin(xyz)

A: Here we will find out the required value.

Q: Contour map of f(x, y). Is fa positive or negative at B?

A: To check whether fx is positive or negative at B, draw a horizontal arrow at B towards the positive…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³ - y°, P(10,…

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Q: Integrate f(x,y) =x+y over the curve C: x² + y = 49 in the first quadrant from (7,0) to (0,7).

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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: Given a surface f(x,y) = -3x² + (3)y². Find the derivative in the direction of v = at the point (5,…

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Q: Determine the gradient and equation of the tangent to the curve f(x, y) = 0 in the point or (a)…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 8, 8) 10…

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Q: Find the differential of f(x,y)=x3+y2−−−−−−f(x,y)=sqrt(x3+y2) at the point (1,2). df =  Then use…

A: Given: The function fx,y=x3+y3 and the point 1,2 The differential to estimate…

Q: 1. For the function f(x, y) = In root (2 + xy), find the equation of the tangent plane at the point…

A: Note: As per the guidelines we are supposed to answer only one question because this is not a…

Q: The gradient of f(x, y) = ry at (x, y) = (3, 1) is %3D

A: Explanation and solutions is given below....

Q: Find a curve in the xy-plane passing through the origin andwhose slope at the point (x, y) is x + y.

A: we have to find a curve in the xy-plane passing through the origin and whose slope at the point (x,…

Q: The temperature at the point (x, y) on a metal plate is modeled by T(x,y)=4e^−(x²+y)/2,x≥0,y≥0. (c)…

A: Given: The temperature at the point x,y on a metal plate is modeled by Tx,y=4e-x2+y2, x≥0, y≥0 To…

Q: (a) Find a function f(x, y) with gradient F, where F = (y cos(xy), x cos(ry) + y² +2y) (b) Use your…

A: (a)According to question given :F→=y cos(xy), x cos(xy)+y2+2yWe have to calculate for f(x,y)As we…

Q: Find a function f(x, y, z) whose level surface f =1 is the graph of the function g(x, y) = 5x + 3y.…

A: Here is the solution of the given problem. Level surface:

Q: Use polar coordinates to find the limit of the function as (x.y) approaches (0,0). 3xy f(x.y) = +y*…

A: We have to find  limit taking x= rcosθ and y = rsinθ

Q: Let f(x.y) = x° +y*. Find the slope of the line tangent to this surface at the point (- 1, - 1) and…

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Q: 1. Determine the directional derivative of the surface f(x, y) = 3x? + y³ at the point P(1,2) in the…

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