Sketch the contour map of the function f(x, y) = 4 – Va2 + y? Label the level curves at c= 4, 3, 2, 1, 0.

Q: The equation of tangent plane to the surface f(x, y, z) = x² + y? +z-9 = 0 at the point (1,2, 4) is…

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Q: The gradient of f(x,y,z) = e*+Ysin z + (y + 1)arccOS x at point %3D will be given by DA (e-2, e, 0).…

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Q: F(x,y,z)=2x2+7y2+7z2 F(x,y,z)= 1152 What is the equation of the tangent to the level surface at…

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Q: (a) Find an equation of the tangent plane to the surface of z = ye(3ry-y²) at (-1, –3, –3). (b)…

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Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = P(1, 4, 8),…

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Q: Describe the level surface F(x, y, z) = 0.…

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Q: Compute F. dr for the oriented curve specified. Jc F(x, y) = (6, y), quarter circle x2 + y? = 1 with…

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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: 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: If the gradient of f is ∇f=y3j−xi+zyk and the point P=(−8,6,2) lies on the level surface f(x,y,z)=0,…

A: To find the equation

Q: The gradient of the tangent to the curve y=flx) at the point P(2, (2)) is given by A 12) – h f(2+k)…

A: To find the gradient of the tangent to the curve y=fx at the point P2, f2.

Q: Sketch a typical level surface for the function. 10) f(x, y, z) = /x2 –z %3D

A: sketch a typical level surface for the following 10) fx,y,z=x2-z it is known that level surface is…

Q: Find the aren of the region in the tirst quadrant baunded by the line y=27, e the line X-4, the…

A: We first sketch the region using a graphing calculator.

Q: Find the tangent plane (Xo, Yo, Zo) from f (x, y) = x² - 3y²; (0,1, -3)

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Q: Classify all level curves of f(x, y) = Vy² – x² and draw its contour map.

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Q: The region bounded by the curves y = r² and y = x³ is rotated around a. the z-axis; b. the y-axis;…

A: the region bounded by the curves y=x2 and y=x3 is rotated around  a) the x-axis b) the y-axis c) the…

Q: Find the equation of the tangent plane to the surface defined by the function f(x, y) = x³…

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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: f(x, y) = Iny –x|, sketch the contour map for the level curve f(x, y) = 0, f(x, y)=1 and f(x, y)= 2.…

A: Given: f(x,y)=ln|y-x2| The objective is to sketch the counter map for level curve f(x,y)=0, f(x,y)=1…

Q: Compute f(X.y) o xI the directional derivative of ait the point (1,1) in a direction ormal to the…

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Q: Find the equation of the tangent plane to the surface z = f ( x , y ) = x 3 − 2 x y + 5 y 2 at P (…

A: Given: The equation of the surface  z=f(x, y)=x3-2xy+5y2. The point P2, 1, 9.

Q: Let f(x,y) = x* + y². Find the slope of the line tangent to this surface at the point (1,1) and…

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Q: A differentiable function f(x,y) has the property that f(2,4)=2 and fx(2,4)=5 and fy(2,4)=−6. Find…

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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: Determine the slope of the tangent line to the curve of intersection of the surface f(x, y) x + 2y x…

A: According to the guidelines, we are answering first question. Please repost the remaining.…

Q: uppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. "rove that dy…

A: Given F(x,y,z)=0

Q: Find the center of mass of the thin plate bounded by the y-axis and the lines y =x and y = 2 - x…

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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: 5. Consider the saddle surface r = y- 2, find the point where the tangent plane is parallel to x+y+z…

A: If two vectors a1, b1, c1 and a2, b2, c2 are parallel, then it can be written that a1, b1, c1=ka2,…

Q: Evaluate the line mtegral over the curve S(-x + y +z) dx + (x+y - z) dy + (x-y +z) dz where the line…

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Q: Justify why the level curves very close to the origin (0,0) for the function f(z, y) = (1-z)(1 – )…

A: As per the instruction, we will be solving the first question. For (1), We are given the function as…

Q: Find equations of the normal plane and tangent line to the curve of intersection of the surfaces…

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Q: Find the linearization of f (x, y, z) = xy / z centered at (2, 1, 2). Use itto estimate f(2.05, 0.9,…

A: Our Aim is to find the linearization of f(x,y,z) =xyz centred at (2,1,2).and then using that value…

Q: Find the tangent plane of the function f(x, y) = √2x² + 2y² at (1,1). Is it parallel to 2- the plane…

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Q: Evaluate f, x*dz + z*dy + y*dx where C is the curve x = t,y = t, z = t? from t= 0 to t= 2.

A: x = t2 ,  y=t2, z=t2 dx = 2t dt,  dy= 2t dt, dz = 2t dt  Putting values in the integral: ∫02t4(2t…

Q: Let f(x, y) = x² + y? and C be the curve along y = x² from (0, 0) to (1, 1).

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Q: Consider the function f defined by f(r,y) = y %3D lim(z,y) (0,0) f(x, y) =

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Q: Consider the function. f(x, y) = 5(y + 1)x² Identify the point(s) on the graph of f at which the…

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Q: Find the plane tangent to the surface given by the function f(x, y) = (x² + y) sen(x - y) + 2x in…

A: Tangent plane  z= f(x0,y0)+fx (x-x0)+fy(y-y0)

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

A: Continuity: Given function is : f(x,y)=x+yx-y The function f(x,y) is defined on S={(x,y)∈R:x,y>0}…

Q: sketch a typical level surface for the function. ƒ(x, y, z) = x + z

A: Given ƒ(x, y, z) = x + z

Q: Civen tz f(x,y) = J 36-9x=y

A: If the graph of z=f(x,y) is sliced by a plane: z=c, then the two dimensional cross-section obtained…

Q: a) Compute the equation of the tangent plane to the level surface 9(x, y, 2) = x’y + 2y°z – 3z°x = 3…

A: First we calculate gradient of g(x,y,z) at point (1,0,-1). Then find equation of tangent plane.

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: 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: Integrate f(x, y) =x+y (4, 0) to (0, 4) over the curve C:x +y 16 in the first quadrant from %3D 32…

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Q: Find the point(s) on the surface at which the tangent plane is horizontal. z = 3 - x2 - y2 + 4y (х,…

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Q: Find the tangent plane and normal line of the surface x+y+z=1 at the point p(0,1,0).

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