# Math Help - newton's method

1. ## 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

2. 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

3. According to Q2

Originally Posted by Angel Rox

Q2 - Evaluate the integral ∫ (1 + sinx)^6 cosxdx by proper substitution.
Substitute z:= sin(x) => z' = cos(x) => $dx = \frac{dz}{z'}$

=> $\int (1+z)^6 cos(x) * \frac{dz}{cos(x)} = \int (1+z)^6 = ...$

4. 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...

5. 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?

6. 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 to get and then sum these two terms seperately... How we r going to do this??

7. 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:
$\sum_{k=1}^n k = \frac{n(n+1)}{2}$

$\sum_{k=1}^n k^3 = \left(\frac{n(n+1)}{2}\right)^2$

8. 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 to get 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.

9. Ok I have thanked him too...Thanx to all of u ...