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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 An example must include either a graph or a specific function (a) For (b) For it not "all" or "no" 3 functions f, f(x)dx is the area between the graph of f and the x-axis on 1K3 functions f, if f(x) is a continuous function, then f (x) dx sf(x)dz functions v, on the interval a <t <b, the integral of the velocity v(t) is the (c) For total distance traveled from t = a to t = b n+1 (d) For real numbers n, / x" dx- n+ 1 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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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. 3 "all" (a) functions f, f(x) dz is the area between the graph of f and the x-axis For on 1s3 4 3 (b) For 'some functions f, if f(a) is a continuous function, then J f(^)drs J /(x) dz 2 2 4 (c) For "some" functions v, on the interval a st s b, the integral of the velocity v(t) is the total distance traveled from t = a to t = b n+1 (d) For "some real numbers n, dz - n+1 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 n +1