Consider F and C below. F(x, y, z) = (2xz + y²)i + 2xyj + (x² + 12z²) k C: x = t², y = t + 3, z = 2t – 1, 0≤t≤1 (a) Find a function f such that F = Vf. f(x, y, z): = =[" C (b) Use part (a) to evaluate Vf. dr along the given curve C.

A company decides to change its floor plan from cubicle to open office. This will bring in a constant stream of $1,000 in extra income annually. If the company invests this extra income in an account that earns 2.5% continuously compounded interest for ten years, is it worth the change? The change in floor plan costs $7,000.

For the function f(x, y, z) =z−x2−y2, describe and sketch a different levelsurface