uestion 14 of 24 For each of the questions below, indicate if the statement is true (T) or false (F). (a) A continuous function on an open interval is integrable. True False (b) A continuous function on a closed interval is integrable. True False (c) If f(x) is continuous on a closed interval [a, b] and /" f(x)dx > 0, then f(x) 2 0 for some x E [a, b]. O True False Roug..pdf

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...
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< Question 14 of 24
For each of the questions below, indicate if the statement is true (T) or false (F).
(a) A continuous function on an open interval is integrable.
True
False
(b) A continuous function on a closed interväl is integrable.
True
False
(c) If f(x) is continuous on a closed interval [a, b] and /" f(x)dx > 0, then f(x) 2 0 for some x E [a, b].
True
False
Paper Roug...pdf
Transcribed Image Text:< Question 14 of 24 For each of the questions below, indicate if the statement is true (T) or false (F). (a) A continuous function on an open interval is integrable. True False (b) A continuous function on a closed interväl is integrable. True False (c) If f(x) is continuous on a closed interval [a, b] and /" f(x)dx > 0, then f(x) 2 0 for some x E [a, b]. True False Paper Roug...pdf
(c) If f(x) is continuous on a closed interval [a, b] and f(x)dx 2 0, then f(x) 2 0 for some x E [a, b].
O True
False
(d) If f(x) and g(x) are integrable on [a, b] and g(x) < f(x) for all x e [a, b], then g(x)dx < f. f(x)dx.
True
False
(e) Every continuous function has an antiderivative.
True
False
Transcribed Image Text:(c) If f(x) is continuous on a closed interval [a, b] and f(x)dx 2 0, then f(x) 2 0 for some x E [a, b]. O True False (d) If f(x) and g(x) are integrable on [a, b] and g(x) < f(x) for all x e [a, b], then g(x)dx < f. f(x)dx. True False (e) Every continuous function has an antiderivative. True False
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