Brilliant

Today Courses

Practice

Algebra
Geometry
Number Theory
Calculus
Probability
Basic Mathematics
Logic
Classical Mechanics
Electricity and Magnetism
Computer Science
Quantitative Finance
Chemistry

Excel in math and science.

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

Quantitative Finance

Numerical Methods

Concept Quizzes

Root Approximation - Bisection
Newton Raphson Method

Newton Raphson Method

Let $f(x) = x^3 - 72x - 220.$ Given that $f(x)=0$ has a root near $x = 12,$ compute $x_1$ by using Newton-Raphson method starting with $x_0=12.$

\frac{919}{90}

\frac{1241}{90}

\frac{379}{45}

\frac{919}{72}

Show explanation

View wiki

by Brilliant Staff

By using the Newton-Raphson method, find the positive root of the following quadratic equation correct to $5$ significant figures: $x^2 + 9x - 5 = 0.$

Start with $x_0 = 2.2.$

2.23607

0.73432

0.52493

1.04986

Show explanation

View wiki

by Brilliant Staff

Use the Newton-Raphson method, correct to $5$ significant figures, to get the root near $x = 2$ of the equation $f(x) = x^3 - 3x - 8.$

2.49203

3.20404

2.13603

2.84803

Show explanation

View wiki

by Brilliant Staff

The equation $f(x) = 4e^x - 12$ has a root near $x = 1.$ Use the Newton-Raphson method to calculate the root correct to $5$ significant figures.

0.96128

0.82396

1.09861

1.23594

Show explanation

View wiki

by Brilliant Staff

Let $f(x) = 4 x^2 - 8.$ Which of the following is the correct representation of $x_{n+1}$ that Newton-Raphson method leads to?

\left( x_n + \frac{1}{2 x_n} \right)

\frac{1}{2} \left( 4 x_n + \frac{2}{ x_n} \right)

2 \left( 4 x_n - \frac{2}{x_n} \right)

\frac{1}{2} \left( x_n + \frac{2}{x_n} \right)

Show explanation

View wiki

by Brilliant Staff

Problem Loading...

Note Loading...

Set Loading...