the problem asks for the limit of f(x) as as x comes from the left of -1. for all x less than or equal to -1, f(x) equals -5. no matter how close x gets to -1 f(x) = -5 so the limit of f(x) from the left of -1 is -5.
for the limit to exist at -1, the limit from the right of -1 must equal the limit from the left of -1.
1/6 p - 4/5
-2/3p + 1/5 - 1 + 5/6p
= -4/6 p + 1/5 - 5/5 + 5/6 p
=(5/6 p - 4/6 p) + (1/5 - 5/5)
= 1/6 p - 4/5
if an object is in motion it will not stop because of inertia, but rather friction and gravity acting upon the object.
hence newton's first law (short version) an object in motion will stay in motion until acted on by an outside force. (i.e friction, gravity.)