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Determine whether the statement is true or false. If it is false, explain why or give...

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Basic Math

Determine whether the statement is true or false. If it isfalse, explain why or give an example that shows it is false.

If f(c) = L,then lim x?c f(x) = L.

False. Define f to be the piece-wise function wheref(x) = x + 3 when x ? ?1 andf(x) = 2 when x = ?1. Then we havef(?1) = 2 while the limit of f as xapproaches ?1 is equal to ?2.

False. Define f to be the piece-wise function wheref(x) = x ? 4 when x ? 2 andf(x) = 0 when x = 2. Then we havef(2) = 0 while the limit of f as xapproaches 2 is equal to ?2.

False. If f(c) = L, then the limit off as x approaches c is equal toL/c.

False. If f(c) = L, then the limit off as x approaches c is equal tocL.

The statement is true.

Answer & Explanation Solved by verified expert
4.3 Ratings (836 Votes)
If fc L then it is FalseWe can see by an example Here So these are not equalDefine f to be the piecewisefunction    See Answer
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