2. Is it possible that x→alim​f(x) does not exist, and x→alim​g(x) does not exist, but x→dlim​[f(x)+g(x)] does exist? Co

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2 Is It Possible That X Alim F X Does Not Exist And X Alim G X Does Not Exist But X Dlim F X G X Does Exist Co 1 (12.78 KiB) Viewed 39 times

2. Is it possible that x→alim​f(x) does not exist, and x→alim​g(x) does not exist, but x→dlim​[f(x)+g(x)] does exist? Consider the functions f(x)=x1​ and g(x)=−x1​. (a) Sketch the graphs (separately) of f(x) and g(x) and find their respective limits as x approaches zero. (b) Sketch the graph of [f(x)+g(x)] and find x→0lim​[f(x)+g(x)].