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Continuity and Discontinuities
256–261 Determine whether the function is continuous at the given value of a. If it’s continuous, state the value at f(a). If it isn’t continuous, classify the discontinuity as a jump, removable, or infinite discontinuity.
256.
where
257.
where
258.
where
259.
where
260.
where
261.
where
262–265 Determine whether the function is continuous at the given values of a. If it isn’t continuous, classify each discontinuity as a jump, removable, or infinite discontinuity.
262.
where
263.
where
264.
where
265.
where
Making a Function Continuous
266–267 Determine the value of c that makes the given function continuous everywhere.
266.
267.
The Intermediate Value Theorem
268–271 Determine which of the given intervals is guaranteed to contain a root of the function by the intermediate value theorem.
268. By checking only the endpoints of each interval, determine which interval contains a root of the function
(A)
(B)
(C)
(D)
(E)
269. By checking only the endpoints of each interval, determine which interval contains a root of the function
(A)
(B)
(C)
(D)
(E)
270. By checking only the endpoints of each interval, determine which interval contains a solution to the equation
(A)
(B)
(C)
(D)
(E)
