Guest RYWIL Posted March 20, 2005 Share Posted March 20, 2005 How do I prove that lim x->a [xf(x) ] = cL, given that Lim x->a f(x) = L? Link to comment Share on other sites More sharing options...
Sayonara Posted March 20, 2005 Share Posted March 20, 2005 Not posting it in the Microbiology forum would be a good start. Thread moved. Link to comment Share on other sites More sharing options...
uncool Posted March 20, 2005 Share Posted March 20, 2005 I assume you mean that lim (x->a) [xf(x) = aL] If lim(x->a) [f(x) = L] There is a neighborhood around a where f(x) is continuous Therefore, there is a neighborhood around a where x f(x) is continuous In the neighborhood, the function returns x f(x) Since both approach finite values, the limit of the product is the product of the limits. Therefore, the limit is aL. -Uncool- Link to comment Share on other sites More sharing options...
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