4) Let F be a field. The derivation f' (T) € F[T] of a polynomial f(T) E a; · Ti e F[T] is defined by i20 f'(T) := E(i- a;) - T*-1. i21 Verify for all f(T) and g(T) in F[T] the rules (F(T) + g(T))' = f'(T) +g'(T) and (f(T) · g(T))' = f'(T) · g(T) + f(T) · gʻ(T).

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Q: 11. Let f(x) be any function with the domain (-o, 0). a) Let e(x) = @)+f(-x), Verify that e(r) is an…

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Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

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Q: 3. Find f. (g) f'(x) = 2x – e

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Q: b) Prove that if f(z) and f(Z) are analytic in a domain I, then I is a constant function.

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Q: Given f(x, y) and y = y(x), we can define a composite functiong(x) = f(x,y(x)).

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