Calculus Multiple Choice - Which of the Following is Not Necessarily True?
Which of the following is NOT necessarily true?
a. There exists a number h in [0,1] such that g(h)
g(x) for all x in [0,1].b. For all a and b in [0,1], if a = b, then g(a) = g(b).
c. There exists a number h in [0,1] such that g(h) = ½.
d. There exists a number h in [0,1] such that g(h) = 3/2.
e. For all h in the open interval (0,1),
g(x) = g(h)
Homework Answers
somewhere, so there is an h s.t. g(h) larger than all otherfunction values.
b true; it is the definition of a function.
c true; a continuous function attains all its values in between,i.e. all values
between zero and one.
d false
e true; This is the definition of continuity
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Calculus Multiple Choice - Which of the Following is Not Necessarily True?
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23. Let be a function defined and continuous on the closed interval (a,b). If f has a relative maximum at cand a<c<b, which of the following statements must be true? 1. f'(c) exists. II. If f'(c) exists, then f'(c)= 0. III. If f'(c) exists, then f"(c)<0. (A) II only (B) III only (C) I and II only (D) I and III only (E) II and III only
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Limits and Continuity 4 Chapter Remark: In the statement of Theorem 4.4.12 we assumed that f was tone and continuous on the interval I. The fact that f is either stric tric. strictly decreasing on / implies that f is one-to-one on t one-to-one and continuous on an interval 1, then as a consequence of the value theorem the function f is strictly monotone on I (Exercise 15). This false if either f is...
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By taking the following problem as being given/true :
(Analysis on Metric Spaces)
Let f : [0, 1] x [0, 1] + R be defined by f(x,y) = ſi if y=x? if y #r? Show that f is integrable on [0, 1] x [0,1]. Let f : [0, 1] + R be uniformly continuous, so that for every e > 0, there exists 8 >0 such that -y<= f(x) - f(y)< € for every I, Y E (0,1). The...
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exists, then so does
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