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JH
Numerade Educator

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Problem 88 Medium Difficulty

Prove Theorem 7.

Answer

$\lim _{n \rightarrow \infty} f\left(a_{n}\right)=f(L)$

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Video Transcript

both here, um, seven states that if the Limited and Ezel and efforts continue settle, then the limit. So this is the statement of the pharaoh. The limit of f of a end as n goes to infinity equals f f l. So the proof for this is very short weaken, right. The limit as n goes to infinity half of an peoples f of the limit is n goes to infinity of a n Why can we do this Since efforts continue Asado This is just the definition of continuity at a point l now on. On the other hand, looking at the inside, we know that the limit of Anna's cell So this justifies the final equation. So we started with the limit of f ve n. We ended up with a f of l. That was the claim that was to be proved. We have proved it. That's our final answer.