# #
#\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!
