1) Show that F is conservative the find a function f such that F = Vf and use that function to evaluate ſ. F· dr along the given curve C. F = (y²z+ 2xz²)i + 2xyzj + (xy² + 2x²z)k, C:x = VE, y = t + 1,z = t²,0

Q: Where are the relative extrema (local maximum and minimum) on the curve? y = 3x² – x A. (0, 0) only…

A: given curve is y=3x2-x3 find the local maxima and local minima

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A: The given problem is to find the equation of tangent plane to the surface and equation of normal…

Q: Find an equation of the tangent plane at the given point. f (x, y) = x/√y,  (4, 4)

A: Given : The function is f ( x, y) = xy and point ( 4, 4 ).

Q: 2.(2.3) Let f(x, y) = xy(e² + e³) for (x, y) = R². (1) Find fx and fy. (2) Find an equation of the…

A: (1) fx​=yex+yey+xyexfy​=xex+xey+xyey (2)(3e)x+(3e)y−z=4e  Explanation:

Q: 2. Derivative of f(x) = - 9x + 4 is: a) 9 b) - 9 c) 4 d) 0

A: Derivative of constant is 0

Q: What is the gradient of the tangent line to the curve y = 2x³ – 3x2 at the point with a = 2? |…

A:

Q: Use Green's Theorem to evaluate F = (xy + y²)i+ (x – y)j | (1, 1) x = y² y = x² (0, 0)

A: we have to evaluate the following by using greens theorem

Q: 17. Let f(x, y) = x'y4. Use Eq. (4) to estimate the change Af = f(2.03,0.9) – f(2, 1)

A: You have to just put the value in the function and proceed....go through the solution

Q: Consider F and C below. F(x, y, z) = yz i+xz j + (xy + 10z) k C is the line segment from (2, 0, -1)…

A: I have explained everything with in the solution. Please go through that.

Q: Pls help ASAP. Pls show all work.

A: Given, y=14 Aim : Find derivative