9514 1404 393
Answer:
D. 5
Step-by-step explanation:
The discontinuities in the tangent function are found where the argument matches π/2 +nπ for some integer n. If x has the range [0, 4], then x² has the range [0, 16]. We're looking for the number of values of n that satisfy ...
0 ≤ π/2 +nπ ≤ 16
Dividing by π gives ...
0 ≤ 1/2 +n ≤ 16/π
Subtracting 1/2, we have ...
-1/2 ≤ n ≤ 4.59...
The integer values of n in this range are {0, 1, 2, 3, 4}. There are 5 of them, hence ...
5 discontinuities in the interval
