Recent questions in Newton's Method

AnalysisAnswered question

Brenda Jordan 2022-11-19

Using impulse formula, derive p_1 i+p_2 i=p_1 f+p_2 f formula where i-is initial state, f-is the final state after collision. Thanks

AnalysisAnswered question

kemecryncqe9 2022-11-12

Averaging Newton's Method and Halley's Method.

Are these two methods identical? / Do they return the same result per iteration?

Are these two methods identical? / Do they return the same result per iteration?

AnalysisAnswered question

Simone Watts 2022-11-09

Difference between Newton's method and Gauss-Newton method

AnalysisAnswered question

Jairo Hodges 2022-11-08

Prove that Newton's Method applied to $f(x)=ax+b$ converges in one step? Would it be because the derivative of $f(x)$ is simply $a$?

AnalysisAnswered question

Maverick Avery 2022-10-23

$dy/dx=\mathrm{sinh}(x)$ A tangent line through the origin has equation $y=mx$. If it meets the graph at $x=a$, then $ma=\mathrm{cosh}(a)$ and $m=\mathrm{sinh}(a)$. Therefore, $a\mathrm{sinh}(a)=\mathrm{cosh}(a)$.

Use Newton's Method to solve for $a$

Use Newton's Method to solve for $a$

AnalysisAnswered question

Emmy Swanson 2022-10-18

Using Newton's method below:

${x}_{n+1}={x}_{n}-\frac{f({x}_{n})}{{f}^{\prime}({x}_{0})}$

using this chord formula where the chord length $c$ is $1$ cm:

$c=2r\mathrm{sin}\frac{\theta}{2}$

supposing the radius is $1.1$ cm and the angle $\theta $ is unknown, show the iterative Newton's Method equation you would use to find an approximate value for $\theta $ in the context of this problem (using the appropriate function and derivative).

${x}_{n+1}={x}_{n}-\frac{f({x}_{n})}{{f}^{\prime}({x}_{0})}$

using this chord formula where the chord length $c$ is $1$ cm:

$c=2r\mathrm{sin}\frac{\theta}{2}$

supposing the radius is $1.1$ cm and the angle $\theta $ is unknown, show the iterative Newton's Method equation you would use to find an approximate value for $\theta $ in the context of this problem (using the appropriate function and derivative).

AnalysisAnswered question

Izabelle Lowery 2022-10-12

Estimate the number of iterations of Newton's method needed to find a root of $f(x)=\mathrm{cos}(x)-x$ to within ${10}^{-100}$.

AnalysisAnswered question

lunja55 2022-09-27

Why the bisection method is slower than Newton's method from a complexity point of view?

AnalysisAnswered question

zementj5 2022-09-25

To find approximate $\sqrt{a}$ we can use Newton's method to approximately solve the equation ${x}^{2}-a=0$ for $x$, starting from some rational ${x}_{0}$.

Newton's method in general is only locally convergent, so we have to be careful with initialization.

Show that in this case, the method always converges to something if ${x}_{0}\ne 0$.

Newton's method in general is only locally convergent, so we have to be careful with initialization.

Show that in this case, the method always converges to something if ${x}_{0}\ne 0$.

AnalysisAnswered question

zapri4j 2022-09-23

Consider the function $f(x,y)=5{x}^{2}+5{y}^{2}-xy-11x+11y+11$. Consider applying Newton's Method for minimizing f. How many iterations are needed to reach the global minimum point?

AnalysisAnswered question

besnuffelfo 2022-09-19

1. If you weigh 140 lbs on Earth, what is your mass in kilograms

2.Using the answer from problem I (hopefully it's correct), determine your weight in Newton's if you were on the moon. Yes, you have to look up something to complete this problem.

3. You measured the mass of a rock to be 355g. What is its weight?

4.You are now holding the rock in your hand from problem 3. What force is the rock on your hand? How much force do you need to exert on the rock to hold in stationary.

2.Using the answer from problem I (hopefully it's correct), determine your weight in Newton's if you were on the moon. Yes, you have to look up something to complete this problem.

3. You measured the mass of a rock to be 355g. What is its weight?

4.You are now holding the rock in your hand from problem 3. What force is the rock on your hand? How much force do you need to exert on the rock to hold in stationary.

AnalysisOpen question

Cyrus Munoz 2022-08-30

For a given function is there a general procedure to find an initial value for ${x}_{1}$ such that Newton's method bounces back and forth between two values forever?

AnalysisOpen question

Jared Irwin 2022-08-30

Can Newton's method be used to guarantee convergence to a global minimum or maximum?

AnalysisOpen question

Bellenik3 2022-08-19

Use newton's method with the specified initial approximation $x1$ to find $x3$, the third appromizmation to the root of the given equation

${x}^{5}-x-1=0$, ${x}_{1}=1$

${x}^{5}-x-1=0$, ${x}_{1}=1$

AnalysisOpen question

betterthennewzv 2022-08-16

Prove, that the direction in Newton's method is a descent direction if the Hessian is positive defnite.

$direction=-H(x{)}^{-1}\ast \mathrm{\nabla}f(x)$prove that this is a descent direction?

$direction=-H(x{)}^{-1}\ast \mathrm{\nabla}f(x)$prove that this is a descent direction?

AnalysisOpen question

Lacey Rojas 2022-08-14

How many iterations must I do for getting $n$ signs after floating point in calculating square root by Newton's method?

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Newton's Method is a powerful tool for solving equations numerically. It is an iterative process that begins with an initial estimate and then converges on the solution, making it ideal for complicated equations. With Newton's Method, users can quickly and accurately find the solution to equations with ease. The method can be used to answer questions such as the roots of polynomial equations, and can even help to solve equations with multiple unknowns. By using Newton's Method, users can save time and effort in finding the answers to their questions. Newton's Method is an invaluable tool for anyone needing help with mathematical equations.