8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at (x,y).

Q: Find a vector function r(t) that describes the curve of intersection be- tween the elliptical…

A: Given To find a vector function r(t) that describes the curve of intersection between the elliptical…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 4x sin(xy)…

A:

Q: Calculate the gradient vector Vf of the function f(x, y) = x² – x + y- x²y – 2y2 at the point (2,1)…

A: According to the given information, it is required to determine the gradient vector of the given…

Q: he vector v = , is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1).  Find a.

A:

Q: The vector n = (2, -3, 6) is normal to the tangent plane to z = h(x, y)at (1, -3, 5). Estimate…

A:

Q: 5. Find the directional derivative of f(x, y) = y² + (x²/y), at the point (2, 1) in the direction of…

A:

Q: Find a vector normal to the surface 3z 3 + x 2 y - y 2 x = 1 at P =(1,-1,1) .

A: Given: 3z3+x2y-y2x=1 at P(1,-1,1)

Q: tangent plane

A:

Q: Consider the function defined by f(x,y) = 4xy - 2x2. Evaluate the directional derivative of f at…

A:

Q: 2. Consider the function f(x, y) = a) Find the directional derivative of f in the direction of the…

A:

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Here we use the formula, Dvf(x,y)=∇f(x,y).v

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A:

Q: 5. For f(x, y) 2x +y v 3i-4j find the rate of change of fat (1,2,6) in the direction of the vector =…

A: rate of change of the function at the given point along the given direction

Q: Find a vector function that represents the curve of intersection of the two surfaces. The cone y = v…

A: Given data: Equation of cone is y=2x2+9z2. Equation of plane is y=5+3z.

Q: Find the directional derivative of the function f(x,v) at point p in the direction of vector a. 1)…

A:

Q: Suppose that z is an implicit function of x and y in a neighborhood of the point P = (0, −3, 1) of…

A: Equation of a line passing through point (a, b, c) and parallel to vector <p, q, r> can be…

Q: Find an equation of the plane tangent to the Bohemian dome S described by the vector function R(u,…

A:

Q: Find the directional derivative of the function f(x, y, z) = xe³ + ye² + zeª at the point (0, 0, 0)…

A: The given function is:f(x,y,z)=xey+yez+zex

Q: Find r'(t), r(t,), and r'(to) for the given value of to. r(t) = (1 + t)i + t°j, to = 1 r'(t) = r(t,)…

A: Here is the solution of the given problem. Space Curve: