Question

If lim x->c f(x)=L, where c is constant then lim x->c (c•f(x))=

Answer 1

By the multiplication rule of limits, if a limit exists and is equal to a finite number, if we multiply our limit by a constant the result will be the limit value times the constant:

`\begin{gathered} \lim_(x\to c)nf(x)=n\lim_(x\to c)f(x) \\ n\in\mathbb{R} \end{gathered}`

Then, applying this property in our problem, we have:

`\lim_(x\to c)cf(x)=c\lim_(x\to c)f(x)=c\cdot(L)=c\cdot L`