Question

Find the root of f(x) = exp(x)sin(x) - xcos(x) by the Newton’s method starting with an...

Find the root of f(x) = exp(x)sin(x) - xcos(x) by the

Newton’s method

starting with an initial value of xo = 1.0.

Solve by using Newton’method until satisfying the tolerance limits of the followings;

i. tolerance = 0.01

ii. tolerance = 0.001

iii. tolerance= 0.0001

Comment on the results!

Homework Answers

Answer #2

answered by: anonymous
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let f(x)=sin(x)+x^3-2. Use the secant method to find a root of f(x) using initial guesses x0=1...
Let f(x)=sin(x)+x^3-2. Use the secant method to find a root of f(x) using initial guesses x0=1 and x1=4. Continue until two consecutive x values agree in the first 2 decimal places.
: Consider f(x) = 3 sin(x2) − x. 1. Use Newton’s Method and initial value x0...
: Consider f(x) = 3 sin(x2) − x. 1. Use Newton’s Method and initial value x0 = −2 to approximate a negative root of f(x) up to 4 decimal places. 2. Consider the region bounded by f(x) and the x-axis over the the interval [r, 0] where r is the answer in the previous part. Find the volume of the solid obtain by rotating the region about the y-axis. Round to 4 decimal places.
Compute three iterations of Newton Raphson method to find the root of the following equations i....
Compute three iterations of Newton Raphson method to find the root of the following equations i. f (x) = x3-x-1 with x0 = 2.5 ii. f (x) = sin(2x)-cos(x)-x²-1 with x0 = 2.0 iii. x exp(x) = 2 with x0 = 0.55
17. I am using Newton’s method to find the negative root of f(x) = 3−x2. (a)...
17. I am using Newton’s method to find the negative root of f(x) = 3−x2. (a) What would be a good guess for x1? Draw the line tangent to f(x) at your x1 and explain why using Newton’s method would lead to the negative root of the function. (b) What would be a bad guess for x1? Draw the line tangent to f(x) at your x1 and explain why using Newton’s method would not lead to the negative root of...
Use Newton's method to approximate a root of f(x) = 10x2 + 34x -14 if the...
Use Newton's method to approximate a root of f(x) = 10x2 + 34x -14 if the initial approximation is xo = 1 x1 = x2 = x3 = x4 =
Find the root of the function f(x) = 8 - 4.5 ( x - sin x...
Find the root of the function f(x) = 8 - 4.5 ( x - sin x ) in the interval [2,3]. Exhibit a numerical solution using Bisection method.
Use Newton's method to derive root of f(x) = sin(x) + 1. What is the order...
Use Newton's method to derive root of f(x) = sin(x) + 1. What is the order of convergence?
Newton's method: For a function ?(?)=ln?+?2−3f(x)=ln⁡x+x2−3 a. Find the root of function ?(?)f(x) starting with ?0=1.0x0=1.0....
Newton's method: For a function ?(?)=ln?+?2−3f(x)=ln⁡x+x2−3 a. Find the root of function ?(?)f(x) starting with ?0=1.0x0=1.0. b. Compute the ratio |??−?|/|??−1−?|2|xn−r|/|xn−1−r|2, for iterations 2, 3, 4 given ?=1.592142937058094r=1.592142937058094. Show that this ratio's value approaches |?″(?)/2?′(?)||f″(x)/2f′(x)| (i.e., the iteration converges quadratically). In error computation, keep as many digits as you can.
Find the root of the function: f(x)=2x+sin⁡(x)-e^x, using Newton Method and initial value of 0. Calculate...
Find the root of the function: f(x)=2x+sin⁡(x)-e^x, using Newton Method and initial value of 0. Calculate the approximate error in each step. Use maximum 4 steps (in case you do not observe a convergence).