Question

If p is a polynomial, then lim x→b p(x) = p(b).
1) True
2) False

Answer 1

The statement is true. If p is a polynomial, then the limit of p(x) as x approaches b will be equal to p(b).

Step-by-step explanation:

The statement is true. If p is a polynomial and we take the limit of p(x) as x approaches b, the limit value will be equal to p(b).

This can be understood by considering the definition of continuity. A polynomial function is continuous over its entire domain, which means that the limit of the function at any point is equal to the value of the function at that point. Therefore, if we take the limit of p(x) as x approaches b, the value will be p(b).

For example, if p(x) = x^2 and we consider the limit as x approaches 3, we would have lim x→3 p(x) = lim x→3 x^2 = 3^2 = 9, which is equal to p(3).