## Donsies 2 years ago Prove using the formal definition of limits: If lim{x->inf} f(x) = -inf and c>0, then lim{x->inf) cf(x) = -inf

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1. Mesa

You use here the theorem which states that limit of product of functions is product of limits of each function: $\lim_{x \rightarrow \infty}[f(x)*g(x)]=[\lim_{x \rightarrow \infty}f(x)]*[\lim_{x \rightarrow \infty}g(x)]$ You have here that g(x)=c, which gives: $\lim_{x \rightarrow \infty}c*f(x)=\lim_{x \rightarrow \infty}c*\lim_{x \rightarrow \infty}f(x)$ Limit of constant is same constant, and limit of function f(x) is given as -inf. You finaly get: $c*(-\infty)=-\infty$

2. Donsies

Ty! :)