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Blackout Cake Blackout Cake
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10 years ago
Use the Intermediate Value Theorem to verify that f(x) has a zero in the given interval. Then use the method of bisections to find an interval of length 1/32 that contains the zero. Round f(x) to six decimal places.

f(x) = cos x - 17x, [0,1]

A) [0.0725,0.0825]
B) [0.03125,0.0625]
C) [0.0825,0.0925]
D) [0.0625,0.0725]
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#1
10 years ago
Similar Question
Use the Intermediate Value Theorem to verify that  f(x)  has a zero in the given Interval for      f(x)  =  x3  -  4x  -  2    in  [-2, -1].


Now    f(-2)  =  -2,   f(-1)  =  +1,
Since f(-2) < 0  and f(-1)  > 0 there exists a root (say  x = c) such that  f(c)  =  0.

Logic:

The Intermediate Value Theorem:   i.e.  follows from continuity of a function
 
Suppose that  f  is continuous on the closed interval  [a,b] and  W  is any number
between  f(a) and f(b).  Then there is a number  c  in [a,b] for which  f(c)  =  W.
The graph below provides a geometric interpretation of the Intermediate Value Theorem.

This theorem is helpful in determining if roots exist in certain ranges for continuous
functions.
 Attached file 
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Blackout C. Author
wrote...
#2
10 years ago
Thank you for your reply!
wrote...
#3
Educator
10 years ago
Hey Blackout Cake, what did you choose as your answer?
Blackout C. Author
wrote...
#4
10 years ago
I chose B) [0.03125,0.0625]. I think it was correct. I don't remember too well because I ended up redoing the assignment and doing at least 100 practice problems.
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