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(a) f(x, y) = 1 √y - x² (b) g(x, y) = 9x² - y² (c) h(x, y) = 4√√x² + y²

(a) f(x, y) = 1 √y - x² (b) g(x, y) = 9x² - y² (c) h(x, y) = 4√√x² + y²

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 1YT
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1. Find the domain and range of the following: 1 (a) f(x, y) = = y-x² 2 (b) g(x, y) = 9-x² - y² (c) h(x, y) = 4√√√x² + y² (d) f(x, y, z) = x + ln y + cos z 1 Y (e) g(x, y, z) = = + x + y Z 2. Provide a sketch of graph of items 1(b) and 1(c). 3. Draw a contour map of f(x, y) = 2xy using level curves at k = -6, -4, 0, 4, 6. 4. Evaluate the following: (a) lim (x,y) →(1,-1) (2x²y+3x²x) 2x² +1 (b) lim (x,y)→(0,0) 1 - x² – 3y² x³y³ 5. Show that lim does not exist. (x,y)→(0,0) 2x¹2 + 3y4
Transcribed Image Text:1. Find the domain and range of the following: 1 (a) f(x, y) = = y-x² 2 (b) g(x, y) = 9-x² - y² (c) h(x, y) = 4√√√x² + y² (d) f(x, y, z) = x + ln y + cos z 1 Y (e) g(x, y, z) = = + x + y Z 2. Provide a sketch of graph of items 1(b) and 1(c). 3. Draw a contour map of f(x, y) = 2xy using level curves at k = -6, -4, 0, 4, 6. 4. Evaluate the following: (a) lim (x,y) →(1,-1) (2x²y+3x²x) 2x² +1 (b) lim (x,y)→(0,0) 1 - x² – 3y² x³y³ 5. Show that lim does not exist. (x,y)→(0,0) 2x¹2 + 3y4
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1. Find the domain and range of the following: 1 (a) f(x, y) = = y-x² 2 (b) g(x, y) = 9-x² - y² (c) h(x, y) = 4√√√x² + y² (d) f(x, y, z) = x + ln y + cos z 1 Y (e) g(x, y, z) = = + x + y Z 2. Provide a sketch of graph of items 1(b) and 1(c). 3. Draw a contour map of f(x, y) = 2xy using level curves at k = -6, -4, 0, 4, 6. 4. Evaluate the following: (a) lim (x,y) →(1,-1) (2x²y+3x²x) 2x² +1 (b) lim (x,y)→(0,0) 1 - x² – 3y² x³y³ 5. Show that lim does not exist. (x,y)→(0,0) 2x¹2 + 3y4
Transcribed Image Text:1. Find the domain and range of the following: 1 (a) f(x, y) = = y-x² 2 (b) g(x, y) = 9-x² - y² (c) h(x, y) = 4√√√x² + y² (d) f(x, y, z) = x + ln y + cos z 1 Y (e) g(x, y, z) = = + x + y Z 2. Provide a sketch of graph of items 1(b) and 1(c). 3. Draw a contour map of f(x, y) = 2xy using level curves at k = -6, -4, 0, 4, 6. 4. Evaluate the following: (a) lim (x,y) →(1,-1) (2x²y+3x²x) 2x² +1 (b) lim (x,y)→(0,0) 1 - x² – 3y² x³y³ 5. Show that lim does not exist. (x,y)→(0,0) 2x¹2 + 3y4
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