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ghaziBest ResponseYou've already chosen the best response.1
where is the function f(c)
 one year ago

lucy4104Best ResponseYou've already chosen the best response.0
c=3, f(x)= (x^2+5)/(x6) continuous or no?... is the question.
 one year ago

ByteMeBest ResponseYou've already chosen the best response.3
at c=3, yes... the function is defined at x=3 so the limit of f is f(3)
 one year ago

lucy4104Best ResponseYou've already chosen the best response.0
what if x=c is not defined?
 one year ago

ByteMeBest ResponseYou've already chosen the best response.3
if f(x) is not defined at x=c, then the limit can still exist but not necessarily at f(c). also, if there is a vertical asymptote at x=c, then the limit does not exist.
 one year ago

lucy4104Best ResponseYou've already chosen the best response.0
the limit can still exist but not necessarily at f(c)?
 one year ago

ByteMeBest ResponseYou've already chosen the best response.3
yes... for example... dw:1361168628388:dw here, the limit of f(x) as x approaches c is a.... NOT f(c)
 one year ago

lucy4104Best ResponseYou've already chosen the best response.0
OHHH so then in that case it would be dicontinuous? When can you tell, or what can you do, to know that something is continuous, but algebraically? step by step and explain?
 one year ago

ByteMeBest ResponseYou've already chosen the best response.3
yes... but in your original function, it is continuous at all x values except at x=6. so in your problem, the limit of f as x approaches c for any value OTHER THAN 6, will be f(c)
 one year ago

lucy4104Best ResponseYou've already chosen the best response.0
oh! so then if x=6 was not an asymptote, but a hole, the limit would be equivalent to f(c)??
 one year ago

ByteMeBest ResponseYou've already chosen the best response.3
***IF*** the function was CONTINUOUS at x=6, then the limit would be f(6)
 one year ago

ByteMeBest ResponseYou've already chosen the best response.3
seems like we're going in circles here but we're not... Continuity of a funtion is defined in terms of limits....
 one year ago

ByteMeBest ResponseYou've already chosen the best response.3
if the "hole" you're referring to is a REMOVABLE discontinuity, then yes, the limit would be f(6) or as you said, f(c)...
 one year ago

lucy4104Best ResponseYou've already chosen the best response.0
yes!!!! ok, thank you!
 one year ago
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