# newton's method

• Dec 30th 2008, 08:35 PM
Angel Rox
newton's method

Q1 - Use Newton's method to find the value of x for the function f(x)=2x^2 + 4x - 3 = 0 ; x > 0
Note : Perform only 3 iterations.

Q2 - Evaluate the integral ∫ (1 + sinx)^6 cosxdx by proper substitution.

Q3 - Evaluate the sum ∑ k(k - 2)(k + 2) using the required theorems.

Note on this sign "∑" on the upper side it is 35 and on the lower side it is k-1....I dont know how to use the tags here coz am new...sorry plz...

Help me in this (Doh)
• Dec 30th 2008, 08:39 PM
Chop Suey
The exact same questions you posted here has been posted elsewhere and already received a response:
http://www.mathhelpforum.com/math-he...t-hw-help.html
• Dec 30th 2008, 08:41 PM
Rapha
According to Q2

Quote:

Originally Posted by Angel Rox

Q2 - Evaluate the integral ∫ (1 + sinx)^6 cosxdx by proper substitution.

Substitute z:= sin(x) => z' = cos(x) => $dx = \frac{dz}{z'}$

=> $\int (1+z)^6 cos(x) * \frac{dz}{cos(x)} = \int (1+z)^6 = ...$
• Dec 30th 2008, 09:01 PM
Angel Rox
Yeah I saw that response which u have mentioned but i couldnt understand his performing methodology because he has just given some simple hints...so if any one could simplify it a lil bit...I'll be thankful...
• Dec 30th 2008, 09:03 PM
Chop Suey
Quote:

Originally Posted by Angel Rox
Yeah I saw that response which u have mentioned but i couldnt understand his performing methodology because he has just given some simple hints...so if any one could simplify it a lil bit...I'll be thankful...

What parts of it you did not understand?
• Dec 30th 2008, 09:09 PM
Angel Rox
I think i can do Q2 by substituting 1+ sinx = u

But in Q 1 which approximation we should take next?

and in Q3 he wrote we need to expand http://www.mathhelpforum.com/math-he...aaa916fe-1.gif to get http://www.mathhelpforum.com/math-he...d83fbd1d-1.gif and then sum these two terms seperately... How we r going to do this??
• Dec 30th 2008, 09:23 PM
Chop Suey
Q1. Try $x_0 = 1$ as Grandad mentioned to find $x_1$, then use $x_1$ to find $x_2$,...,then use $x_n$ to find $x_{n+1}$

Q3. The lower side should read k=1.

And what Grandad meant is that once you have expanded it to:
$\sum_{k=1}^{35} (k^3 - 4k)$

Separate it into: $\sum_{k=1}^{35} k^3 - 4\sum_{k=1}^{35} k$

Recall that:
$\sum_{k=1}^n k = \frac{n(n+1)}{2}$

$\sum_{k=1}^n k^3 = \left(\frac{n(n+1)}{2}\right)^2$
• Dec 30th 2008, 09:37 PM
Chop Suey
Quote:

Originally Posted by Angel Rox
I think i can do Q2 by substituting 1+ sinx = u

But in Q 1 which approximation we should take next?

and in Q3 he wrote we need to expand http://www.mathhelpforum.com/math-he...aaa916fe-1.gif to get http://www.mathhelpforum.com/math-he...d83fbd1d-1.gif and then sum these two terms seperately... How we r going to do this??

And thank Grandad as well. His post was sufficient for your question and my reply was based on it.
• Dec 30th 2008, 09:40 PM
Angel Rox
Ok I have thanked him too...Thanx to all of u ... :)