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g(x) = sin(x) + cos(.5x) on (-4, 4)
Okay, so for the above expression, I have to:
a) Calculate an expression for the 5th derivative g^(5)(x).
b) Find a bound for the absolute value of g^(5)(x) on the interval indicated.
c) Use Taylor's Theorem to find a cap for the error; that is, a cap for the difference between the function and the Maclaurin polynomial of degree four on the interval.
I did part a and this is what I got:
g'(x) = cos(x)-.5sin(.5x)
g''(x) = -.25cos(.5x) - sin(x)
g'''(x) = .125sin(.5x) - cos(x)
g^(4)(x) = .0625cos(.5x) + sin(x)
g^(5)(x) = cos(x) - .03125sin(.5x)
I guess my biggest problem is finding the bound for the interval (-4, 4) (part b). I know how to find a cap for the error, but in order to do that, I have to find the bound first. I'm not really sure about the procedure to finding the bound. I've been reading about it for hours, but my book doesn't really give any clear examples. Any help would be GREATLY appreciated.
Last edited by virtualinsanity (2007-03-23 03:51:13)
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