Solved: Use Newton's method to find solutions accurate to within 10-5 to the following

Chapter 2, Problem 2

(choose chapter or problem)

Use Newton's method to find solutions accurate to within \(10^{-5}\) to the following problems

\(\begin{array}{l}\text{a. } \quad 1-4 x \cos x+2 x^{2}+\cos 2 x=0, \quad \text{ for } 0 \leq x \leq 1\\ \text{b. } x^{2}+6 x^{5}+9 x^{4}-2 x^{3}-6 x^{2}+1=0 \text{, for } -3 \leq x \leq-2\\ \text{c. } \sin 3 x+3 e^{-2 x} \sin x-3 e^{-x} \sin 2 x-e^{-3 x}=0, \quad \text{ for } 3 \leq x \leq 4\\ \text{d. } e^{3 x}-27 x^{6}+27 x^{4} e^{x}-9 x^{2} e^{2 x}=0, \quad \text{ for } 3 \leq x \leq 5\end{array}\)