6. Determine if the following statements are true or false. If true, explain why. If false, either provide an example which disproves the statement, or explain why. a. Let f be a strictly increasing function on the interval [0,1]. For any number of rectangles chosen, then right endpoint area approximation is greater than the left endpoint area approximation b. Let g be a strictly decreasing function on the interval [0,1]. The right endpoint area approximation where the number of rectangles is n = 2, is greater than the right endpoint area approximation where the number of rectangles is n = 6. 1 For the definite integral| -dx, if approximating the area using left endpoints and n = 3 rectangles, the x4 + 6 c. width of the rectangles would be an integer value. 2 아-([m)' d. Iffis continuous on [a, b], then (f(x))* : f(x)

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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6. Determine if the following statements are true or false. If true, explain why. If false, either provide an example
which disproves the statement, or explain why.
Let f be a strictly increasing function on the interval [0,1]. For any number of rectangles chosen, then right
endpoint area approximation is greater than the left endpoint area approximation
а.
b. Let g be a strictly decreasing function on the interval [0,1]. The right endpoint area approximation where the
number of rectangles is n = 2, is greater than the right endpoint area approximation where the number of
rectangles is n = 6.
1
For the definite integral
-dx, if approximating the area using left endpoints and n = 3 rectangles, the
+ 6
с.
x4
width of the rectangles would be an integer value.
2
d. If fis continuous on [a,b], then | (fx)) =
f(x)
a
Transcribed Image Text:6. Determine if the following statements are true or false. If true, explain why. If false, either provide an example which disproves the statement, or explain why. Let f be a strictly increasing function on the interval [0,1]. For any number of rectangles chosen, then right endpoint area approximation is greater than the left endpoint area approximation а. b. Let g be a strictly decreasing function on the interval [0,1]. The right endpoint area approximation where the number of rectangles is n = 2, is greater than the right endpoint area approximation where the number of rectangles is n = 6. 1 For the definite integral -dx, if approximating the area using left endpoints and n = 3 rectangles, the + 6 с. x4 width of the rectangles would be an integer value. 2 d. If fis continuous on [a,b], then | (fx)) = f(x) a
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