Answer:
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.