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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Thanks Prof D.

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salamat din sir

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[@tanjamesfrancismiguela.1694]

thank you po prof D. from stem 1207

[@chacha122]

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

[@dianedomingo11uzumestem73]

Pano po pag fraction ung given

[@shellamaylatagan]

how to factors?

[@Jesus_Saves_HCR2]

Paano po kapag hindi binigay yung value ni x?

[@mochamartin6869]

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

[@pisqueraangel2287]

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

[@cheesedog1523]

(2) same question sir sana masagot mo'to

[@marygracemendoza2894]

bakit ba kasi ako nag stem🥲

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You speak different languages

[@MerakiDraw]

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

[@cheesedog1523]

(2)

[@hazeljhoydelmundo7937]

[@user-ti7ns5ud7i]

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

[@madisuzuya6049]

hindi naman kase yan variable

[@madisuzuya6049]

yang x² - 4 is algebraic equation since may variable jan need mo sya i factor out

[@madisuzuya6049]

di naman pwede i factor out if number lets say 2² - 4 pano mo ifafactor out yan

[@bastesfjraymund6862]

Paano po nangyari yung 2+2? 8:41

[@dadadadaniela1434]

substitue po ang value ng x which is 2 sa x+2

[@michaelvaldez8269]

thank you sir