I came across the attached question in our calculus book. The limits in question are:
F(x), which approaches 0 from the left and 1 from the right as x goes to 2
J(x), which approaches 1 from the left and 0 from the right as x goes to 2.
Question B) ii. asks for the limit of [F(x) + J(x)] as x goes to 2. The left hand limits add up to 1, and the right hand limits do too, so the limit is 1 as x approaches 2 - the answer key matches this.
However, in C) ii., which asks for limit of [F(x)J(x)] as x approaches 2, the left hand limits multiply to 0 and the right hand limits multiply to 0, but the answer key has DNE. Am I missing something completely about how limits work? Or is the answer key wrong?
Thanks in advance! Edited photo of the page