Troubleshooting Newton's Method for f(x) and g(x)

[RadiationX]

i have the answer to this problem i just see why I'm not getting the same answer as my solution manuel. i Have two functtions f(x) = x and g(x) = tan(x)
and i have to find where these two functions are equal using Newtons method.
i subtracted the two functions to get this new function H(x) = x -tan(x) then i found the differential of this new function to be 1 - sec^2 (x). now by looking at the given graph of the first two functions i estimated the soulution to be about 4.1. then by unising Newtons method i calculated two iterations and got an answer of 8.5987, which is wrong the answer is 4.493. what could i be doing wrong? i know how to use Newtons method.

 

[Muzza]

You need to use a better first approximation.

 

[NateTG]

i have the answer to this problem i just see why I'm not getting the same answer as my solution manuel. i Have two functtions f(x) = x and g(x) = tan(x)
and i have to find where these two functions are equal using Newtons method.
i subtracted the two functions to get this new function H(x) = x -tan(x) then i found the differential of this new function to be 1 - sec^2 (x). now by looking at the given graph of the first two functions i estimated the soulution to be about 4.1. then by unising Newtons method i calculated two iterations and got an answer of 8.5987, which is wrong the answer is 4.493. what could i be doing wrong? i know how to use Newtons method.

Are you sure that the two functions are only equal in one place? x and tan x intersect in *lots* of places.

 

[RadiationX]

x has to be between pi/2 and 3pi/2 these are the asmyspotes.

 

[BobG]

You need to use a better first approximation.

You need a real good first approximation, otherwise it never converges. If you know that the tangent of 3 pi/2 is undefined and start a little lower than that, you're okay. If your guess is less than around 4.29, you won't converge.

 

[RadiationX]

thanks guys the last reply helped me out.