I need to check my work with an expert, to make sure I got my answer correct and to check if my work is correct.

1. Use Newton's method to approximate a root of the equation 4x^3+5x^2+4=0 as follows: Let x1=1 be the initial approximation. The second approximation x2 is and the third approximation x3 is 2. Use Newton's method to approximate a root of the equation 4x^7+5x^4+2=0 as follows: Let x1=3 be the initial approximation. The second approximation x2 is and the third approximation x3 is 3. Use Newton's method to approximate a root of the equation cos(x27)=x3 as follows. Let x1=1 be the initial approximation. The second approximation x2 is The third approximation x3 is 4. Find the positive value of x which satisfies x=4.100sin(x). Give the answer to four decimal places of accuracy.

(Remember to calculate the trig functions in radian mode!)