11.1
Let g(x, y) = cos(x + 5y). (a) Evaluate g(10, −2). (b) Find the domain of g. (c) Find the range of g. (Enter your answer using interval notation.)
(a) g(10, −2) = 1 (b) R² (c) [-1,1]
Sketch the graph of the function. f(x, y) = y² + 4
Bent paper
Find and sketch the domain of the function. f(x, y) = √(3x − y)
Checker board
Find and sketch the domain of the function. f(x, y) = arcsin(x² + y² − 5)
Concentric circles
Draw a contour map of the function showing several level curves. f(x, y) = ye^(4x)
Converging lines
Draw a contour map of the function showing several level curves. f(x, y) = x³ − 5y
Layered, positive cubic functions
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Sphere
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The level surfaces are a family of parallel planes.
Sketch the graph of the function. f(x, y) = 12 − 4x − 5y
Triangle