[68] If f and g are continuous at a, then (f±g), kf, fg, and f/g (g(a) ≠ 0) are also continuous at a.

https://www.evernote.com/shard/s29/sh/3fcdc42d-51c7-4a10-bcc6-fc92934cccab/e6961d8bef7b69e03322719b33afe0e9

[67] lim (f(x)±g(x)) = lim f(x) ± lim g(x), lim kf(x) = k・lim f(x)

https://www.evernote.com/shard/s29/sh/e1df7638-806c-4c0a-82dc-546accd11a3f/74aae0c20585ba39a252273f05de493f

[66] An arbitrary subsequence converges to a ⇒ The original sequence also converges to a.

https://www.evernote.com/shard/s29/sh/c6c652d7-537a-4f44-b9bb-595e06ac8ffb/f472ef9a3cfec9b8694e2f8d351ace0d

[65] If lim f(x) = b and lim g(x) = c, then lim f(x)・g(x) = bc, and lim f(x)/g(x) = b/c (if c≠0)

https://www.evernote.com/shard/s29/sh/e64a8d45-e3e6-43d4-acf9-33cb06bde025/14b2da255367f352d204c48031c58900

[64] f(x)→b (x→a) ⇔ ∀ε＞0. ∃δ＞0. f(U(a,δ)∩D) ⊂ U(b,ε) ／ ∃lim f(x) (x→a) ⇒ f is bounded in some neighborhood of a in D.

https://www.evernote.com/shard/s29/sh/9860ca20-334f-4ace-a06b-18088739686a/d946b21aa1c8c0a051d32350191171ec

[63] f is continuous at a ⇔ . . . （関数fは点aにおいて連続である）

https://www.evernote.com/shard/s29/sh/1328340f-e265-4a4b-ba89-6c75fde634dd/83f6cf4e58ff752b66372941b56cb591

[62] ∃limf(x) ⇒ ∃!limf(x).

https://www.evernote.com/shard/s29/sh/c96ef008-7316-4a37-a263-cda7ef498811/7b92cac8e8cec3343adf7566a2177e5d