Continuity of a function | Determining whether a function is continuous at a number | @Prof D

Basic Calculus
Continuity of a function at a number

A function is said to be continuous on the interval [a,b] if it is continuous at each point in the interval. Note that this definition is also implicitly assuming that both f(a) and limx→af(x) lim x → a ⁡ exist. If either of these do not exist the function will not be continuous at x=a .

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Thank You Guys!

[cenizamaricar]

thank you po hehe nakalimutan ko na to pero u bring me back to life 😂❤

[pisqueraangel]

Sa number 3 po, hindi po ba ifa-factor out yung nasa 1st condition...??
Para hindi sya maging 0/0?

[chacha]

good eve, prof d! anong type po ng discontinuity yung number 3? thank you in advance po:)

[Jesus_Saves_HCR]

Paano po kapag hindi binigay yung value ni x?

[MerakiDraw]

what if yung denaminator is like x² - 2 at yung itaas eh x -4?
same process din po ba?

[HappyMukwasa-zg]

At questions 3
Why didn't you factor out at the first, but you foctored out at the second step.

[mochamartin]

Prof D, how can I can I prove this using epsilon-delta proof? lim 4/(x - 1) as x --> 3 = 2