Question 1 Describe and sketch the level surfaces of the functions a) f(x, y, z) = Vx²+y²+z? and b) g (x, y, z) = z2 – x? – y2 The value of f is the distance from the origin to the point in 3-dim space (x, y, z). Each level surface Vx2+y²+z² = c >0 is a sphere of radius c centred at the origin. What are coordinates of origin? Describe the level curves in the x - y plane and in the x – z plane. Sketch a typical level surface for the function. The level surfaces of constant c g will be different for c = 0, c > 0 and c < 0. Read back through notes to see in which cases the surfaces are cones or hyperboloids

Q: If u = and , then what is the magnitude of 2 + . Round to the nearest hundredth. Answer:

A:

Q: sider the surface z = f(z, y)=√√/25 - 1² - y².

A:

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

A:

Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

Q: Match each parametrization with the corresponding surface. (i) (ii) (iii) (iv) (v) Answer Bank (u,…

A:

Q: 2) Draw contour maps for functions f(x, y) = x² - 4y², and g(x, y) = x² + 4y². What shape. are these…

A: The contour of function f(x,y) represents parabolas.

Q: Describe the image of the line z = 1 + iy under the map flz) = sin z %3D

A:

Q: Find foF dr where C is a circle of radius 3 in the plane x+y+z= 8, centered at (1, 3, 4) and…

A:

Q: (10) Let f(x, y) = /x-y a) Find the domain and range of f (x, y). Sketch the domain on the x-y…

A: Step:-1 Given that fx, y =x-y Part (a):- The square root function is real when x-y≥0 x-y≥0⇒x≥y⇒y≤x…

Q: Describe and draw at least 3 level surfaces for the function f(r, y, z) = x²+ y? - z?

A:

Q: Consider the function f(x, y, z) = 3x² + y² - 4z. i) A contour surface S passes through the point A…

A: To find the value of the contour surface passing through the point A = (2, 3, -1), we need to…

Q: Verify Stokes' theorem for the helicoid (1, 0) = First, compute the surface integral: = (VF)…

A: Given surface is helicoid whose vector parametric equation is \)" data-mce-style="cursor:…

Q: a) Mark the points on the contours where Iz = 0. b 2.

A: A contour line or level curve is the intersection of a surface with a horizontal plane. For example…

Q: 2.Proof that any tangent plane for the surface F(- point = 0 passses through a fixed

A: Given below clear explanation

Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.