Let n E N and f:RR: f(x)= x^. Let c R and g: R ...

 

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Let n E N and f:R⇒R: f(x)= x^. Let c € R and g: R → R: g(x) = c. (i) Prove that for every & E R we have limx→g f(x) = §”. (ii) Prove that for every & E R we have limx→g g(x) = = C. (iii) Let co, C₁,..., Cm E R and P: R⇒R: P(x) = co + c₁x + that lim→ P(x) = P(§). (iv) Let do, d₁..., dn E R and Q: R → R: Q(x) = do + d₁x + that if Q() # 0, then P(x) lim x→ Q(x) P(E) Q(૬) Cmx. Prove • dnxn. Prove Let n E N and f:R⇒R: f(x)= x^. Let c € R and g: R → R: g(x) = c. (i) Prove that for every & E R we have limx→g f(x) = §”. (ii) Prove that for every & E R we have limx→g g(x) = = C. (iii) Let co, C₁,..., Cm E R and P: R⇒R: P(x) = co + c₁x + that lim→ P(x) = P(§). (iv) Let do, d₁..., dn E R and Q: R → R: Q(x) = do + d₁x + that if Q() # 0, then P(x) lim x→ Q(x) P(E) Q(૬) Cmx. Prove • dnxn. Prove

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i To prove that lim x fx we need to show that for every M 0 there exists a number N 0 such that for ... View the full answer