left at x = 5.)FIGURE N2–9
In Examples 26 through 31, we determine whether the functions are continuous at the points
specified:
EXAMPLE 26
Is continuous at x = −1?
SOLUTION: Since f is a polynomial, it is continuous everywhere, including, of course, at x =
−1.EXAMPLE 27
Is continuous (a) at x = 3; (b) at x = 0?
SOLUTION: This function is continuous except where the denominator equals 0 (where g has
an infinite discontinuity). It is not continuous at x = 3, but is continuous at x = 0.EXAMPLE 28
Is continuous(a) at x = 2; (b) at x = 3?
SOLUTIONS:
(a) h(x) has an infinite discontinuity at x = 2; this discontinuity is not removable.
(b) h(x) is continuous at x = 3 and at every other point different from 2. See Figure N2–10.