I just learned advanced mathematics, too. I hope these are helpful to you.
When 1.x approaches 3,
Because this is a piecewise function, we can find the limit when x approaches 3+ and 3- respectively.
X approaches 3+ lim f(x)=lim x+ 1=4.
X approaches 3- lim f(x)=lim 7-x=4.
Because the above results are equal, the limit is 4 when x approaches 3.
2. when x approaches 0, f (x) = 7-x.
So lim f(x)=7.