Posted by Sam on Thursday, March 17, 2011 at 2:43am.
For the function y=(e^2x)+(3x)-(10), use Newton's method and the calculator method to find the x value for which y=15. Please show your work so that I can understand the question! Thank you so much!! it means alot!!
- Calculus! - Reiny, Thursday, March 17, 2011 at 9:23am
so you are solving
e^(2x) + 3x - 25 = 0
let y = e^(2x) + 3x - 25
y' = 2e^(2x) + 3
newtons's formula says
X = x - f(x)/f'(x)
where x is your starting x value and X is the new value.
Hopefully your X will approach x, when that happens you have the solution.
X = x - (e^(2x) + 3x - 25)/(2e^(2x) + 3)
= (2xe^(2x) - e^(2x) + 25)/(2e^2(2x) + 3)
I made a rough sketch of y = e^(2x) + 3x - 25
and noticed that there was an x-intercept, which would be your solution, at appr x = 1.5
So I will make that my starting x
X ---- x
1.50951695 -- 1.509515688
1.509515688 -- 1.50951688
Wow, got the answer correct to 9 decimal places after only 3 iterations.
The key thing is that you start with an initial guess close to the real number.
Answer This Question
More Related Questions
- calculus - Use Newton's method to solve the equation sec x = 4 in the interval x...
- Calculus-Newton Method Approximation - Use Newton's method to approximate the ...
- calculus - Hello! Just needed help with understanding this specific question. We...
- Calculus - You are using Newton's method to solve e^x - 2. If you first guess ...
- Calculus - Use Newton's Method with the function f(x)=x^2-2 and initial value Xo...
- unique solution - How do I show that the equation x^4 + 3x + 1 = 0, -2 <= x &...
- Calculus - Use Newton's Method to approximate the positive root of the function ...
- College Math II - Solve by any method. x(x + 1) = 12 I am not sure what method ...
- Calculus 1 Newton's Method - Using Newton's method, approximate the root of the ...
- calculus - Find the interval which contains a zero for the given function. The ...