CadyMath

#1. Use 1 steps of Newton's Method to estimate the solution to the equation. Use the given starting value.
\(\sqrt{2x-1}=0,\quad x_0=3,\quad x_1=\)

\(-1.801\)

\(-2\)

\(-3.801\)

\(9\)

#2. Use 2 steps of Newton's Method to estimate the solution to the equation. Use the given starting value.
\(x^5+4x^4+6x^3-3x^2+4x+4=0,\quad x_0=-3,\quad x_2=\)

\(-1.461\)

\(0\)

\(1.639\)

\(\frac{2}{3}\)

#3. Use 2 steps of Newton's Method to estimate the solution to the equation. Use the given starting value.
\(-x^4+x^3+4x^2+6x-3=0,\quad x_0=-2,\quad x_2=\)

\(-0.386\)

\(-\frac{5}{7}\)

\(-\frac{7}{3}\)

\(0\)

#4. Use 1 steps of Newton's Method to estimate the solution to the equation. Use the given starting value.
\(2\cos\left(2x-5\right)=0,\quad x_0=-1,\quad x_1=\)

\(-1.404\)

\(-1.574\)

\(-\frac{10}{7}\)

\(2.978\)

#5. Use 2 steps of Newton's Method to estimate the solution to the equation. Use the given starting value.
\(\csc\left(2x-3\right)=0,\quad x_0=5,\quad x_2=\)

Newton's Method fails.

\(-23.188\)

\(-34.618\)

\(11.43\)

#6. Use 1 steps of Newton's Method to estimate the solution to the equation. Use the given starting value.
\(\sec\left(2x-6\right)=0,\quad x_0=-4,\quad x_1=\)

\(-3.931\)

\(-6.785\)

\(-\frac{1}{5}\)

\(\frac{1}{5}\)