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: 3. Calculate the directional derivative of the function f : R³ → R, defined by f(x, y, z) = y²+xz at…

A: Step 1: Step 2: Step 3: Step 4:

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: 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 all points on the curve r(t) = ti + t²j+t³k where its tangent line is parallel to the vector…

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: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

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: