7. (a) Graph the function f(x) = VT- x². (b) Graph the function f(x, y) = /1– x² – y². (Hint: Let z = /1-x2 - y?, and then square both sides of the equation.) (c) The graph of the function f(x, y, z) = /1 – x² – y2 – z4 is half of a hypersphere of dimension 3. Explain why "hypersphere" is a good name for the graph and why the graph is only half of the hypersphere. What equa- tion defines the entire hypersphere? (d) Fill in the blanks: The graph of the function f(x1,x2 ...,xn) = /1 – x² – x}- .,Xn) /1 – x² – x3 - ·x² is half of -. .. - a of dimension in

7. (a) Graph the function f(x) = VT- x². (b) Graph the function f(x, y) = /1– x² – y². (Hint: Let z = /1-x2 - y?, and then square both sides of the equation.) (c) The graph of the function f(x, y, z) = /1 – x² – y2 – z4 is half of a hypersphere of dimension 3. Explain why "hypersphere" is a good name for the graph and why the graph is only half of the hypersphere. What equa- tion defines the entire hypersphere? (d) Fill in the blanks: The graph of the function f(x1,x2 ...,xn) = /1 – x² – x}- .,Xn) /1 – x² – x3 - ·x² is half of -. .. - a of dimension in

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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