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November 1st, 2011, 03:42 PM  #1 
Newbie Joined: Nov 2011 Posts: 1 Thanks: 0  need help with linear approximation problem
Use linear approximation to estimate the value of f(3.1), given that f(3)=9 and f '(x) = (5x^2) / (sqrt(x^32)) Please help ! 
November 2nd, 2011, 12:32 AM  #2 
Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8  Re: need help with linear approximation problem
f(x+dx) = f(x) + ( f ' (x) )*dx approximately x+dx = 3.1 x =3 dx =0.1 f(x) = f(3) = 9 compute f ' (x) = f ' (3) thanks to the given formula then compute f(x) + ( f ' (x) )*dx 
November 2nd, 2011, 01:33 AM  #3 
Senior Member Joined: Oct 2011 From: India ???? Posts: 224 Thanks: 0  Re: need help with linear approximation problem Let . Then: Integral becomes 
November 2nd, 2011, 01:35 AM  #4 
Senior Member Joined: Oct 2011 From: India ???? Posts: 224 Thanks: 0  Re: need help with linear approximation problem
Sorry I went wrong with the last step. 
November 2nd, 2011, 03:11 AM  #5 
Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8  Re: need help with linear approximation problem
Hello Etyucan, you forgot the integration constant. The correct analytical result is : 9+(10/3)sqrt[(x^3)2]  (10/3)sqrt[(3^3)2] = (10/3)sqrt[(x^3)2] (23/3) = 9.90572329283767 for x=3.1 But isn't what pdeep needs to answer to his problem. Linear approximation is much simpler and suffisant : the resul is close to the exact value. 

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