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m180.09.08

# m180.09.08 - 2.5 Continuity Homework 1 State the three part...

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Unformatted text preview: 2.5 Continuity Homework 1. State the three part deﬁnition of continuity. 2. Give the values where the function is discontinuous. State which requirements from the three part deﬁnition of continuity fail. 7 6. Determine the values of a and b that make the given function continuous. if x < 0 if x = 0 f (x) = a b cos x if x > 0 Use continuity to evaluate the limit of the function. √ 5+ x 7. lim √ x→4 5+x 8. x→π sin(x + sin x) lim 2 sin x x Section 2.5 cont. The Intermediate Value Theorem 3. Give the values where the function is discontinuous. State which requirements from the three part deﬁnition of continuity fail. Math 180 Weds. 9/08/2010 9. Let f (x) = x5 + 7x4 + 5x3 + 2x2 + 9x − 10. A table of values of this function is given below. f (x) x −8 −6610 −7 −1690 −6 224 620 −5 −4 434 170 −3 −2 20 −16 −1 0 −10 1 14 2 200 3 980 Circle the interval(s) which must contain a zero of the function f . [−8, −7], [−7, −6], [−6, −5], [−5, −4], [−4, −3], [−3, −2], [−2, −1], [−1, 0], [0, 1, ], [1, 2], [2, 3] 4. Sketch the graph of the function. Give the values where the function is discontinuous. State which requirements from the three part deﬁnition of 1 continuity fail. f (x) = at x = 1 x−1 5. Sketch the graph of the function. Give the values where the function is discontinuous. State which requirements from the three part deﬁnition of continuity fail. x2 if x < 2 if x = 2 f (x) = 3 3x − 2 if x > 2 ...
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