lim_(x->oo) (sqrt(3x-5)+sqrt(2x+7))?

1 Answer
Feb 28, 2018

\lim _{x\to \infty }(\sqrt{3x-5}+\sqrt{2x+7})\ =\ infty

Explanation:

\lim _{x\to \infty }(\sqrt{3x-5}+\sqrt{2x+7})

According to the limit property, we have:

\lim_{x\to a}[f(x)\pm g(x)]=\lim_{x\to a}f(x)\pm \lim _{x\to a}g(x)

=\lim_{x\to\infty\:}(\sqrt{3x-5})+\lim_{x\to\infty\:}(\sqrt{2x+7})

According to the limit property, we have:

\lim_{x\toa}[f(x)]^b=[\lim_{x\toa}f(x)]^b

=\sqrt{\lim_{x\to\infty\:}(3x-5)}+\sqrt{\lim_{x\to\infty\:}(2x+7)}

\text{Apply Infinity Property:}

\lim_{x\to\infty}(ax^n+\cdots+bx+c)=\infty ," " a>0\ \ \ ,\ \ \ \text{n is odd}

=\sqrt{\infty }+\sqrt{\infty }

\text{Apply Infinity Property:} " "\infty ^c=\infty

=infty+infty

=infty


That's it!