3.Givens a function 𝑓(𝑥, 𝑦) and a positive number 𝜀 as
Group 1,4,7: 𝑓(𝑥, 𝑦) = (𝑥+𝑦)
2+cos 𝑥
, 𝜀 = 0.02.
Group 2,5,8: 𝑓(𝑥, 𝑦) = (𝑥+𝑦) , 𝜀 = 0.01.
𝑥2+1
Group 3,6: 𝑓(𝑥, 𝑦) = 𝑦
𝑥2+1
, 𝜀 = 0.05.
Show that there exists a 𝛿 > 0 such that for all (𝑥, 𝑦),
√𝑥2 + 𝑦2 < 𝛿 ⇒ |𝑓(𝑥, 𝑦) − 𝑓(0,0)| < 𝜀.
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