Suppose f :U ⊆ Rn → R is not defined at a point a ∈ Rn but is defined for all x near a....

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 B_r is just an open ball of radius r centered at a with the point a deleted.) Then we say lim_x→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 ∈ B_r ), then f (a) > N.

(a) Using intuitive arguments or the preceding technical definition, explain why lim_x→0 1/x² =∞.

(b) Explain why

(c) Formulate a definition of what it means to say that

(d) Explain why