Q: Suppose that for all xE(0,5), f(x) is between 1+x and 3+sin((pi)(x)). Find lim x->2 f(x).

Is this question related to the intermediate value theorem? It is confusing me, can anyone help out? I am not certain of what xE(0,5) is defining, is that a set of x values or am I mistaken?

clearly (0,5) is is a set of x values, since x is in that interval. I'm sure it is just to restrict us to a single period of 2π.

1+x <= f(x) <= 3+sin πx
as x->2,
1+2 <= f(x) <= 3