Use Newton's method with initial approximation x1 = −1 to find x2, the second approximation to the root of the equation x3 + x + 8 = 0. (Round your answer to four decimal places.) x2 =

The second approximation to the root of the equation is -1.5000.

Step-by-step explanation:

The Newton's method is a numerical method by approximation that help find roots of a equation of the form with the help of the equation itself and its first derivative. The Newton's formula is:

Where:

- i-th approximation, dimensionless.

- (i+1)-th approximation, dimensionless.

- Function evaluated at the i-th approximation, dimensionless.

- First derivative of the function evaluated at the i-th approximation, dimensionless.

The function and its first derivative are and , respectively. Now, the Newton's formula is expanded:

If , the value of is:

The second approximation to the root of the equation is -1.5000.

b is the final answer! : )

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.