Each of Exercises 73–78 gives a function f(x, y) and a positive num- ber ɛ. In each exercise, show that there exists a 8 > 0 such that for all (х, у), Vx² + y² < & = |f(x, y) – f(0, 0)| < ɛ. 73. f(x, y) = x² + y², ɛ = 0.01 74. f(x, y) = y/(x² + 1), ɛ = 0.05 75. f(x, y) = (x + y)/(x² + 1), ɛ = 0.01 76. f(x, y) = (x + y)/(2 + cos x), ɛ = 0.02 xy2 77. f(x, y) = and f(0, 0) = 0, ɛ = 0.04 x³ + y4 x² + y? 78. f(x, y) and f(0, 0) = 0, ɛ = 0.02

Each of Exercises 73–78 gives a function f(x, y) and a positive num- ber ɛ. In each exercise, show that there exists a 8 > 0 such that for all (х, у), Vx² + y² < & = |f(x, y) – f(0, 0)| < ɛ. 73. f(x, y) = x² + y², ɛ = 0.01 74. f(x, y) = y/(x² + 1), ɛ = 0.05 75. f(x, y) = (x + y)/(x² + 1), ɛ = 0.01 76. f(x, y) = (x + y)/(2 + cos x), ɛ = 0.02 xy2 77. f(x, y) = and f(0, 0) = 0, ɛ = 0.04 x³ + y4 x² + y? 78. f(x, y) and f(0, 0) = 0, ɛ = 0.02

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 32E

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