Suppose f :U ⊆ Rn → R is not defined at a point a ∈ Rn but is defined for all x near a. In other words, the domain U of f includes, for some r > 0, the set Br = {x ∈ Rn | 0 < ||x – a|| < r }. (The set Br is just an open ball of radius r centered at a with the point a deleted.) Then we say limx→a f (x) = +∞ if f (x) grows without bound as x → a. More precisely, this means that given any N > 0 (no matter how large), there is someδ > 0 such that if 0 < ||x – a|| < δ (i.e., if x ∈ Br ), then f (a) > N.
(a) Using intuitive arguments or the preceding technical definition, explain why limx→0 1/x2 =∞.
(b) Explain why
(c) Formulate a definition of what it means to say that
(d) Explain why
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