f the statement is always true, explain why. If not, give a counterexample. f f
ID: 2885672 • Letter: F
Question
f the statement is always true, explain why. If not, give a counterexample. f f is a function such that lim f(x) exists, then (0) exists Choose the correct answer below O A. The statement is not always thue. For exahon lim ox) - but) does not exist O B. The statement is always true. It is always the case that lim x)-) O C. The statement a ahenys true Athough it is possibie for 80) to exist without lim fe) existing it is not possible for im x) t exist wlthout f0) also existing. OD. The statenort is nt always tue. For example, itfo--.ten limfa)#0but to) does not oust to select your answerExplanation / Answer
Limit of a function at 'a' is the behaviour of the function on the left hand side and right hand side of the 'a'. Function may or may not be defined at the point 'a'.
As given in the Option A. It is not always true that f(0) exists when limit is defined at 0. As given function x2/x is not defined at 0 but limit is equal to 0 at point 0. Hence Option A is correct.
Counter example is not correct in option D.
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