State the domain and range of the function f(x, y, z) Draw a quick, yet reasonably...

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State the domain and range of the function f(x, y, z) Draw a quick, yet reasonably accurate graph of the following function. Label your axes in the usual (right handed) orientation. f(x, y) = x² + y² Find and sketch the level curves f(x, y) = c on the same set of coordinate axes for the given values of c. Label your curves. f(x, y) = x-y-2 c= 3, 1, 0, 1, 3 - Evaluate the limit. 1 x² + y² + z2 lim (x, y) (0, 0) y 4+x² - x - xy + 3 lim (x, y) (1, -1) x 2y + 5xy - y ³ 3 By considering different paths of approach, show that the function has no limit as (x, y) → (0, 0). (HINT: approach along the x-axis and the y-axis). Use accurate and appropriate notation. y4 - 2x² ap Əx Draw the branch (or tree) diagram, and write the chain rule formula for and where p = k(r, s, t), r = h(x, y), s = f(x, y), and t = g(x, y). 218 ay dw Find for w = xy + z if x = cost, y = sint, and z = t. dt Əw Find when r = 8 and s = - 8 if w = (x+y+z) 2₁ x=r-s, y = cos(r + s), and z = sin (r + s). ar 3 Assuming that 2x ³ + 6y2 - 3xy = 0 defines y as a differentiable function of x, dy Fx use the theorem dx Fy == to find dy dx at (1, 1). Determine if F = (2x − 3)i - zj + (cosz)k is conservative or not conservative. If it is conservative, then find the potential function. State the domain and range of the function f(x, y, z) Draw a quick, yet reasonably accurate graph of the following function. Label your axes in the usual (right handed) orientation. f(x, y) = x² + y² Find and sketch the level curves f(x, y) = c on the same set of coordinate axes for the given values of c. Label your curves. f(x, y) = x-y-2 c= 3, 1, 0, 1, 3 - Evaluate the limit. 1 x² + y² + z2 lim (x, y) (0, 0) y 4+x² - x - xy + 3 lim (x, y) (1, -1) x 2y + 5xy - y ³ 3 By considering different paths of approach, show that the function has no limit as (x, y) → (0, 0). (HINT: approach along the x-axis and the y-axis). Use accurate and appropriate notation. y4 - 2x² ap Əx Draw the branch (or tree) diagram, and write the chain rule formula for and where p = k(r, s, t), r = h(x, y), s = f(x, y), and t = g(x, y). 218 ay dw Find for w = xy + z if x = cost, y = sint, and z = t. dt Əw Find when r = 8 and s = - 8 if w = (x+y+z) 2₁ x=r-s, y = cos(r + s), and z = sin (r + s). ar 3 Assuming that 2x ³ + 6y2 - 3xy = 0 defines y as a differentiable function of x, dy Fx use the theorem dx Fy == to find dy dx at (1, 1). Determine if F = (2x − 3)i - zj + (cosz)k is conservative or not conservative. If it is conservative, then find the potential function.

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