Let f and g be real-valued functions defined on (b, ∞). Suppose that limx->∞f(x)=L and limx->∞g(x)=M, where L, M ∈ ℝ . Prove the following... (a) limx->∞(f+g)(x)=L+M (b) limx->∞(fg)(x)=LM (c) If , then limx->∞(kf)(x)=kL (d) If  for  and , then limx->∞(f/g)(x)=L/M

Let f and g be real-valued functions defined on (b, ∞). Suppose that lim_x->∞f(x)=L and lim_x->∞g(x)=M, where L, M ∈ ℝ .

Prove the following...

(a) lim_x->∞(f+g)(x)=L+M

(b) lim_x->∞(fg)(x)=LM

(c) If , then lim_x->∞(kf)(x)=kL

(d) If  for  and , then lim_x->∞(f/g)(x)=L/M