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Explain why the following statements are true or false. a) If f(x) is continuous at x...

Explain why the following statements are true or false.

a) If f(x) is continuous at x = a, then lim x → a f ( x ) must exist.

b) If lim x → a f ( x ) exists, then f(x) must be continuous at x = a.

c) If lim x → ∞ f ( x ) = ∞ and lim x → ∞ g ( x ) = ∞ , then lim x → ∞ [ f ( x ) ⋅ g ( x ) ] = ∞

d) Given f(x) of degree n and g(x) of degree n + 1, and if lim x → ∞ f ( x ) = ∞ and lim x → ∞ g ( x ) = ∞ , then lim x → ∞ (f(x)/g(x))=1

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