Hello,
[tex]\displaystyle \lim_{x\rightarrow7^+} \ {(3+\sqrt{2+x})}=3+\sqrt{2+7}=3+\sqrt{9}=3+3=6\\\\ \lim_{x\rightarrow7^-} \ {(8-\sqrt{x-3})}=8-\sqrt{7-3}=8-\sqrt{4}=8-2=6[/tex]
It means that
[tex]\text{Step 1 *** }\displaystyle \lim_{x\rightarrow7^+} \ f(x) \text{ exists and its value is }6 \\ \\\text{Step 2 *** }\displaystyle \lim_{x\rightarrow7^-} \ f(x) \text{ exists and its value is }6\\\\\text{Step 3 *** The two limits are equals so we can conclude that } \\ \\ \displaystyle \boxed{\lim_{x\rightarrow7} \ f(x) \text{ exists and its value is }6}[/tex]
Thanks
