Find a upper bound

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  • #1
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help me, please

if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f(4)(x))


Thanks
 

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  • #2
tiny-tim
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Welcome to PF!

Hi ZuzooVn! Welcome to PF! :smile:
if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f(4)(x))
ok … draw y = sin(x).

Now turn the paper sideways and draw x = sin(y) …

what do you get? :wink:
 
  • #3
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Hi ZuzooVn! Welcome to PF! :smile:


ok … draw y = sin(x).

Now turn the paper sideways and draw x = sin(y) …

what do you get? :wink:
Would u please tell me more detail about your solution????
 
  • #4
tiny-tim
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Would u please tell me more detail about your solution????
Nope! o:)

Just do it! :smile:
 
  • #5
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Nope! o:)

Just do it! :smile:
Please

Because, i didn't know how to find the upper bound
 
  • #6
HallsofIvy
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tiny-tim has suggested a first step. Have you done it yet?
 
  • #7
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tiny-tim has suggested a first step. Have you done it yet?
yes, i have done it .

But because i'm a Vietnamese, so my English skill isn't good :D
 
  • #8
HallsofIvy
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Excellent! Thank you.

Now, tiny-tim, what in the world are you talking about? I'm afraid I dont' see your point either.

I would probably use "brute strength"

If y= sin(sin(x)), then y'= -cos(sin(x))(-cos(x))= cos(x)cos(cos(x)). Now, instead of actually doing the other derivatives (because they get really messy!), use the fact that the nth derivative of (f(x)g(x)) will be [itex]\sum _nC_i f^{i}g^{n-i}[/itex] to see that we will, after three more derivatives, have a sum of 4 terms with binomial coeficients times sin and cos- and the largest possible value for sine or cosine is 1.
 
  • #9
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Unless I made a silly mistake typing things in, it appears that Wolfram Alpha thinks it should be around 3.76.
 
  • #10
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help me, please

if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f(4)(x))


Thanks
You need to define what f(4)(x) means. Do you mean, the fourth iteration of f on x, i.e. f o f o f o f (x)? Or do you mean (as others have interpreted) the fourth derivative of f?
 
  • #11
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You need to define what f(4)(x) means. Do you mean, the fourth iteration of f on x, i.e. f o f o f o f (x)? Or do you mean (as others have interpreted) the fourth derivative of f?
I means the fourth derivative of f
 
  • #12
HallsofIvy
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Unless I made a silly mistake typing things in, it appears that Wolfram Alpha thinks it should be around 3.76.
Do you mean least upper bound? I get 8 as an upper bound.
 

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