Please help with these questions from Math 151, with a details explanation please.

Thank you so much.

1.

Use Newton's method to approximate a root of the equation 5:137 + 53:4 + 4 = 0 as follows. Let :31 : 3 be the initial approximation. The second approximation :32 is l | and the third approximation 3:3 is l ' Carry at least 4 decimal places through your calculations. Use Newton's method to approximate a root of the equation :33 + a: + 4 = 0 as follows. Let :31 = 1 be the initial approximation. The second approximation :32 is l | and the third approximation :33 is l ' Use Newton's method to approximate a root of the equation 3:133 + 252 + 2 = 0 as follows. Let $1 = 1 be the initial approximation. The second approximation :32 is i i , and the third approximation 3:3 is i i Use Newton's method to approximate a root of the equation 5 sin(a':) : a: as follows. Let 231 = 1 be the initial approximation. The second approximation :32 is i ' and the third approximation mgis ' ' Use Newton's method to approximate a root of the equation cos (x* + 3) = x as follows. Let x1 = 1 be the initial approximation. The second approximation 2isUse Newton's method to approximate a root of the equation 80.932 : 3 :13 as follows. Let :31 : 2 be the initial approximation. The second approximation :32 is l ' and the third approximation mgis ' ' Use Newton's method to approximate a root of the equation In (5x) = arctan(x - 0.2) as follows. Let x1 = 0.1 be the initial approximation. The fourth approximation x4 is and the fifth approximation x5isUse Newton's Method to estimate a root of the function f (2:) : :1: + 5 em Use the initial estimate :31 = 0.6: 1131 : 0.6 1132: 53 w I l 53 Hi. | | 5'3 cu l l 5'3 a: l l 53 -..1 | | Use Newton's Method to estimate an intersection of the functions f(x) = -3x - 1 and g(x) = tan x Use the initial estimate x1 = -0.2608: 1 = -0.2608 03 =