17. Let g be a continuous function on the closed interval [0,1]. Let g(0) =1 and g(1) = the following is NOT necessarily true? (A) There exists a number h in [0,1] such that g(h) > g(x) for allx in [0,1]. (B) For all a and b in [0,1], if a = b, then g(a) = g(b). 1 (C) There exists a number h in [0,1] such that g(h) =÷. 2 3 (D) There exists a number h in [0,1] such that g(h)=- 2 (E) For all h in the open interval (0,1), lim g(x)= g(h). 18. If y" = 2y' and if y= y' = e when x = 0, then when x=1, y= (A) +1) (B) e (C) (D) (I 1-cos?(2x). 19. lim (A) -2 (В) 0 (C) 1 (D) 2
17. Let g be a continuous function on the closed interval [0,1]. Let g(0) =1 and g(1) = the following is NOT necessarily true? (A) There exists a number h in [0,1] such that g(h) > g(x) for allx in [0,1]. (B) For all a and b in [0,1], if a = b, then g(a) = g(b). 1 (C) There exists a number h in [0,1] such that g(h) =÷. 2 3 (D) There exists a number h in [0,1] such that g(h)=- 2 (E) For all h in the open interval (0,1), lim g(x)= g(h). 18. If y" = 2y' and if y= y' = e when x = 0, then when x=1, y= (A) +1) (B) e (C) (D) (I 1-cos?(2x). 19. lim (A) -2 (В) 0 (C) 1 (D) 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![17. Let g be a continuous function on the closed interval [0,1]. Let g(0) =1 and g(1) = 0. 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).
1
(C) There exists a number h in [0,1] such that g(h) =÷.
3
(D) There exists a number h in [0,1] such that g(h) =-
2
(E) For all h in the open interval (0,1), lim g(x)= g(h).
xh
18. If y" = 2y' and if y= y' = e when x = 0, then when x=1, y=
(A) +1)
(² -e)
(В) е
(C)
(D)
(E)
1-cos?(2x)
19. lim
(A) -2
(В) 0
(C) 1
(D) 2
(E) 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe1a7199-658c-4cc8-8192-abb8f25301d9%2Fa63f3009-ec0b-45c3-9d9c-262c4608826b%2F0m5qj5f_processed.png&w=3840&q=75)
Transcribed Image Text:17. Let g be a continuous function on the closed interval [0,1]. Let g(0) =1 and g(1) = 0. 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).
1
(C) There exists a number h in [0,1] such that g(h) =÷.
3
(D) There exists a number h in [0,1] such that g(h) =-
2
(E) For all h in the open interval (0,1), lim g(x)= g(h).
xh
18. If y" = 2y' and if y= y' = e when x = 0, then when x=1, y=
(A) +1)
(² -e)
(В) е
(C)
(D)
(E)
1-cos?(2x)
19. lim
(A) -2
(В) 0
(C) 1
(D) 2
(E) 4
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