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4. Fill in the blank with "all", "no", or "some" to make the following statements true. Note that "some" means one or more instances, but not all. • If your answer is "all", then give a brief explanation as to why. • If your answer is "no", then give a brief explanation as to why. • If your answer is "some", then give two specific examples that illustrate why your answer it not "all" or “no". An example must include either a graph or a specific function. (а) For functions f, f(x) dx is the area between the graph of f and the x-axis on 2 < x < 4. (b) For functions f, if f(x) is a continuous function, then f(2) dæ s f(x) dæ. (c) For total distance traveled from t = a to t = b. functions v, on the interval a

4. Fill in the blank with "all", "no", or "some" to make the following statements true. Note that "some" means one or more instances, but not all. • If your answer is "all", then give a brief explanation as to why. • If your answer is "no", then give a brief explanation as to why. • If your answer is "some", then give two specific examples that illustrate why your answer it not "all" or “no". An example must include either a graph or a specific function. (а) For functions f, f(x) dx is the area between the graph of f and the x-axis on 2 < x < 4. (b) For functions f, if f(x) is a continuous function, then f(2) dæ s f(x) dæ. (c) For total distance traveled from t = a to t = b. functions v, on the interval a

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 10TFE
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4. Fill in the blank with "all", "no", or "some" to make the following statements true. Note that "some" means one or more instances, but not all. • If your answer is "all", then give a brief explanation as to why. • If your answer is "no", then give a brief explanation as to why. • If your answer is "some", then give two specific examples that illustrate why your answer it not "all" or "no". An example must include either a graph or a specific function. 4 (а) For functions f, f(x) dx is the area between the graph of f and the x-axis on 2 < x < 4. 1 2 (b) For functions f, if f(x) is a continuous function, then f(x) dæ s f (x) dx. (c) For total distance traveled from t = a to t = b. functions v, on the interval a st< b, the integral of the velocity v(t) is the | x" dx xn+1 + C. n + 1 (d) For real numbers n, In mathematics, we consider a statement to be false if we can find any examples where the statement is not true. We refer to these examples as counterexamples. Note that a counterexample is an example for which the “if" part of the statement is true, but the "then" part of the statement is false.
Transcribed Image Text:4. Fill in the blank with "all", "no", or "some" to make the following statements true. Note that "some" means one or more instances, but not all. • If your answer is "all", then give a brief explanation as to why. • If your answer is "no", then give a brief explanation as to why. • If your answer is "some", then give two specific examples that illustrate why your answer it not "all" or "no". An example must include either a graph or a specific function. 4 (а) For functions f, f(x) dx is the area between the graph of f and the x-axis on 2 < x < 4. 1 2 (b) For functions f, if f(x) is a continuous function, then f(x) dæ s f (x) dx. (c) For total distance traveled from t = a to t = b. functions v, on the interval a st< b, the integral of the velocity v(t) is the | x" dx xn+1 + C. n + 1 (d) For real numbers n, In mathematics, we consider a statement to be false if we can find any examples where the statement is not true. We refer to these examples as counterexamples. Note that a counterexample is an example for which the “if" part of the statement is true, but the "then" part of the statement is false.
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