Answer to Question #222940 in Calculus for Nikhil Singh

Question #222940
Show that lim (|x| +1)= ∞
x→∞
1
Expert's answer
2021-08-04T16:41:20-0400

limx(x+1)=?x is positive when x. Therefore x=x.=limx(x+1)Applying Infinity property:limx(axn+...+bx+c)=a>0, n is odda=1, n=1hence=thus limx(x+1)=\lim\limits_{x\to\infin}(|x|+1)=?\newline x\ is\ positive\ when\ x\to\infin.\ Therefore\ |x|=x.\newline =\lim\limits_x(x+1)\newline Applying\ Infinity\ property: \newline \lim\limits_{x\to\infin}(ax^{n}+...+bx+c)=\infin\newline a>0,\ n\ is\ odd\newline a=1,\ n=1\newline hence=\infin\newline thus\ \lim\limits_{x\to\infin}(|x|+1)=\infin


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