Question

Help ASAP this question is hard

Answer 1

Hello,

`\displaystyle \lim_(x\rightarrow7^+) \ {(3+√(2+x))}=3+√(2+7)=3+√(9)=3+3=6\\\\ \lim_(x\rightarrow7^-) \ {(8-√(x-3))}=8-√(7-3)=8-√(4)=8-2=6`

It means that

`\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}`

Thanks