Question

Dada a função ()= responda e justifique:


a) Existe (−1)?

b) Existe $\lim_{x \to \--1+} f(x)?$

c) Existe $\lim_{x \to \--1-} f(x)$?

d) A função é contínua em =−1?

Answer 1

Explicação passo-a-passo:

 derivatives

I've been trying to solve the following problem:

Suppose that ff and f′f′ are continuous functions on RR, and that limx→∞f(x)limx→∞f(x) and limx→∞f′(x)limx→∞f′(x) exist. Show that limx→∞f′(x)=0limx→∞f′(x)=0.

I'm not entirely sure what to do. Since there's not a lot of information given, I guess there isn't very much one can do. I tried using the definition of the derivative and showing that it went to 00 as xx went to ∞∞ but that didn't really work out. Now I'm thinking I should assume limx→∞f′(x)=L≠0limx→∞f′(x)=L≠0 and try to get a contradiction, but I'm not sure where the contradiction would come from.

Could somebody point me in the right direction (e.g. a certain theorem or property