University:
Seattle Pacific University
Course:
MAT 1236 | Calculus III
Academic year:

2024
Views:

282

Pages:

1
Author:

trescandogss

Workshop #13 1. For each function, sketch the graph. The sketch some traces and some level curves. Identify which are which. (a) f (x, y) = e−x (b) f (x, y) = 25 − x2 − y 2 p (c) f (x, y) = 25 − x2 − y 2 2. Draw a contour map of the function showing several level curves. (a) f (x, y) = x − y + 2 (b) f (x, y) = x2 + 4y 2 (c) f (x, y) = xy (d) f (x, y) = ln(y − 4x) 16 (e) f (x, y) = 2 x + y2 √ (f) f (x, y) = y − x 3. Sketch a typical level surface. (a) f (x, y, z) = x2 + y 2 + z 2 (b) f (x, y, z) = z − x2 − 4y 2 p 4. Let f (x, y) = x2 + y 2 and g(x, y) = x2 + y 2 . Sketch level curves for each function for k = 0, 1, 4, 9. How are the graphs of f and g different? 5. Consider the curve C given by x2 + y 2 = 1. Find a function f (x, y) and a constant k so that C is the level curve of f with value k. How many choices of f and k are there?