How do I prove that lim x->a [xf(x) ] = cL, given that Lim x->a f(x) = L?

Not posting it in the Microbiology forum would be a good start.

 

Thread moved.

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-