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June 10th, 2014, 06:10 AM  #11 
Newbie Joined: Apr 2014 From: Singapore Posts: 7 Thanks: 0 
Btw, I realised that while the values are close, the gradients are rather different. Is there any way to make the gradients similar too? Thanks 
June 10th, 2014, 07:45 AM  #12 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,266 Thanks: 2434 Math Focus: Mainly analysis and algebra 
The limit as $n \to \infty$ of the Fourier Series is the original function $sin{x}$. So at the limit the gradients and the values are the same. In other words, you should take more terms. Of course, the closer you get to $x = n\pi$ the greater the dfference in the gradient, because $sin{x}$ is not smooth at $x = n\pi$ while the Fourier Series is smooth everywhere. 
June 11th, 2014, 04:43 AM  #13 
Newbie Joined: Apr 2014 From: Singapore Posts: 7 Thanks: 0 
Btw, I realised that while the values are close, the gradients are rather different. Is there any way to make the gradients similar too? Thanks 
June 11th, 2014, 04:59 AM  #14 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,097 Thanks: 703 Math Focus: Physics, mathematical modelling, numerical and computational solutions  

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function, positive, sine, smooth, strictly 
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