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anonymous
 3 years ago
is lim as x approaches c the same as f(c)?
anonymous
 3 years ago
is lim as x approaches c the same as f(c)?

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0where is the function f(c)

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0at c=3, yes... the function is defined at x=3 so the limit of f is f(3)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0what if x=c is not defined?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0if 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.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the limit can still exist but not necessarily at f(c)?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes... for example... dw:1361168628388:dw here, the limit of f(x) as x approaches c is a.... NOT f(c)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0OHHH 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?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes... 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)

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0***IF*** the function was CONTINUOUS at x=6, then the limit would be f(6)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0seems like we're going in circles here but we're not... Continuity of a funtion is defined in terms of limits....

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0if the "hole" you're referring to is a REMOVABLE discontinuity, then yes, the limit would be f(6) or as you said, f(c)...

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes!!!! ok, thank you!
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