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

Q: The slope of the surface z = xy² in the x-direction at the point (2, 3) is _____, and the slope of…

A: Given:z=xy2   x-directionat the point 2, 3 y-directionat the point 2,3

Q: Find a function f (x, y) that has the line y = 3x - 4 as a level curve.

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: (b) Compute the slope of the line that is parallel to the xz-plane and tangent to the surface z = x…

A: Given: Let's calculate the slope of the line tangent to the surface z=x(x+y) at the point that is…

Q: Draw a contour map of the function showing several level curves. f(x, y) = xy

A: To draw contour map of   f (x,y) = xy

Q: Sketch in the two level curves of: f (x, y) = y+ x² = k _for k = 1, 2.

A: Solution is written in below steps.

Q: f(x, y, z) = x² + 3y² + 5z?

A: Let us assume f(x,y,z)=x2+3y2+5z2=k Assume that k≠0 x2+3y2+5z2=k Divide both sides by k,…

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 an equation of the plane tangent to the graph of g(r, y) = 3ev²-z² at the point where (x, y) =…

A:

Q: Compute F• dr for the oriented curve specified. F(x, y) = (9, y), quarter circle x² + y2 = 1 with x…

A: Given:

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

A:

Q: Find the plane tangent to f(x,y)=x/(x+y) at the point (1,5).

A:

Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

Q: Find the equation for the tangent plane to the surface Z =-8x² - 3y2 at the point (2 1, -35). O 2x +…

A: We can find the answer as below

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

A:

Q: find the tangent plane to the surface z = y-x at the point (1,2,1)

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Q: Find the positively oriented simple closed curve C for which the value of the line integral C(y^3…

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Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: Find an equation of the tangent plane to the surface z = x2 + y2 + 3 at the given point( 2, 1, 8).

A: Known fact: Let F(x,y,z) be the surface which is differentiable at P(x0, y0, z0). then the equation…

Q: f(7,9) = 7. (1,1,1) zx/2+ y/2+5 -4/8-y/2

A:

Q: Compute F. dr for the oriented curve specified. F(x, y) = (9, y), quarter circle x² + y2 = 1 with x…

A:

Q: Find the equation of the tangent plane to the surface z = 4 号+ゾ + y² at the point (2, -3, 10)

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Q: Sketch a smooth connected curve y = f(x) with f(-2) = 8, f(0) = 4, f(2) = 0, f'(2) = f'(-2) = 0, %3D…

A:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

A:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y2,…

A: This question is based on finding equation of tangent plane.

Q: ) Draw a contour map of f(x,y)=x^2+4y^2 with an appropriate contour interval, showing at least six…

A: Solution of the problem as follows

Q: Sketch the contour plot of f(x, y) = 4x² + y² using level curves of height k = 0, 1, 2, 3, 4, 5.

A: Given: f(x,y)=4x2+y2 Let 4x2+y2=k. Now graph contour plot for k=0,1,2,3,4,5.

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 an equation of the tangent plane to the surface at the given point. f(x, y) = (1, 5, 5)

A: Given: The function is fx,y=yx, 1,5,5. The objective is to find an equation of the tangent plane to…

Q: (b)Let f(x, y) = /3x +2y. %3D Find the slope of the surface z = f(x, y) in the x-direction at the…

A: (b) Slope of z= f(x,y) in the y- direction at the point (4,2) Slope ofz in the y - direction means…

Q: Find the slope of the surface z = f (x, y) in the y-direction at the point (64, 8).

A: Follow the procedure given below.

Q: Find the points on the graph of f(x, y) = 3x 2 - xy - y 2 at which thetangent plane is horizontal.

A: Given that, fx, y=3x2-xy-y2z=3x2-xy-y2

Q: Let C be the curve on the xy-plane that is the projection of a horizontal cross-section of the…

A: Given surface is,yz=ln(x+z) zxy=1x+z(1+zx)y-1x+zzx=1x+zzx=1y(x+z)-1 Take the derivative with respect…

Q: Draw a contour map of the function f (x,y) = (y – 2x)2 showing several level curves.

A:

Q: Find the points on the curve x2 + xy + y2 = 1 in the xy-plane that are nearest to and farthest from…

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Q: Calculate the geodesic curve of the surface x^2 +y^2 -z=0

A:

Q: 4) Suppose that the level curves of a function z = f (x, y) consists of straight lines. Must the…

A: Given that level curve of a function z=f(x,y) consists of straight lines.

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = 2, (1, 4, 4) 10 z…

A: f(x,y)=y/x

Q: Find an equation of the tangent plane to the surface at the given point. z = x2 + y2 + 4, (1,2, 9)

A: We know that the equation of tangent plane to the curve z=f(x,y) at point (a,b,c) is

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: Compute F• dr for the oriented curve specified. F(x, y) = (9, y), quarter circle x² + y² = 1 with xs…

A:

Q: Find the slopes of the surface in the x- and y-directions at the given point.

A: It is given that,z=xy  and point (1,2,2). We have to find the slopes of the surface in the x- and…

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 an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y²,…

A:

Q: Find an equation of the tangent plane to the surface z = √(x2 + y2), at the given point (3, 4, 5).

A: We have given equation z=x2+y2 First we rearrange the equation of the surface into the form fx,y,z=0…

Q: Let f(x, y) = x2 + 2y. Sketch the level curves for f = −2, 0, 1.

A: Level curves: A level curve is defined as the cross section of the graph of z=fx,y taken at a…

Q: What is the largest vertical distance between the graphs of the functions y = Vx and y = x² in the…

A:

Q: Sketch the reglon enclosed by the glven curves. x = 6y2, x = 4 + 5y2 y y 2- 2- 10 15 20 10 15 20 -1…

A: Here we have,  x=6y2 ............................................. (1) and, x=4+5y2…