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March 6th, 2011, 02:33 PM  #1 
Member Joined: Feb 2011 Posts: 58 Thanks: 0  require a value of h such that sin(x) equals for x
I have a bunch of these types of questions which are all similar, could someone show me how to do this one, then I will be able to do the rest. Find a value of h such that for where 
March 6th, 2011, 09:41 PM  #2 
Senior Member Joined: Nov 2010 Posts: 502 Thanks: 0  Re: require a value of h such that sin(x) equals for x
I assume you are learning Taylor series and Taylor expansions?

March 8th, 2011, 07:03 AM  #3 
Member Joined: Feb 2011 Posts: 58 Thanks: 0  Re: require a value of h such that sin(x) equals for x
yes

March 8th, 2011, 10:51 AM  #4 
Senior Member Joined: Nov 2010 Posts: 502 Thanks: 0  Re: require a value of h such that sin(x) equals for x
Ok, so the general idea behind these questions is to look at the Taylor remainder form. The so called Lagrange form involves looking at the next term in the series (the first one excluded), and maximizing the derivative coefficient. As we are dealing with sin, the derivative cannot be larger than 1. So we need only consider x^7/7! < .0001. This looks to be about .9 to me. I was deliberately a little hazy on the details to encourage you to work through it. But does that make sense? Do you know the Lagrange form? 

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