a) Sketch and label the contours z = 0, z =±1, and +4 for the function z = f(x, y) = -x² + y?. Plot the gradient vector field F = Vf. b) Plot the vector field F(x, y) = (y,0).

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 the domain of the vector function r(t)=⟨ln⁡(19t),sqrt(t+8),1/sqrt(7−t)⟩ using interval…

A: Given vector function isrt=ln19t,t+8,17-tfind the domain.

Q: Find the GPA for the student: Course Credits Grade Points English 3 C 2.0 Philosophy 4 A 4.0 Science…

A:

Q: Let r(t) = (-3t5 - 1, 2e³, 4 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 T(0) -

A: If  is vector valued function which is differentiable and then the unit tangent of is given by

Q: Suppose that f(z,y) is differentiable, and suppose that the directional derivative of f at the…

A:

Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.

A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

Q: Find a equation vector and the equation of the tangent line at the point P0 where t=0.2 on the graph…

A: The tangent is the line that just touches the curve at the point. The equation for the tangent line…

Q: 2) Sketch the curve with the vector equation r(t) = costi- costj+ sin tk. Show the direction of…

A:

Q: Why is r(t) = ⟨ƒ(t), g(t), h(t)⟩ called a vector-valued function?

A: Given r(t) = ⟨ƒ(t), g(t), h(t)⟩. We need to give reason why r(t) is called vector-valued function.