Find the root of the equation tanx + tanhx = 0 which lies in the interval (1.6, 3.0) correct to four significant digits using the method of false position.
1- use bisection method to find out the positive sequare root of 30 correct to 4 decimal places.
2- solve by iteration method
(1) 1+log x =x/2
(2) Sin x = x+1/x-1
(3) X^3 - 2x^2 - 5 =0
3- Find the smallest root of the equation
1 - x + x^2/(2!)^2 - x^3/(3!)^2 + x^4/(4!)^2 - x^5/(5!)^2 + .................. = 0
To approximate the value of f'''(xk), the following formulas are used
f'''k =1/h^3[ fk+3 −3 fk+2 +3 fk+1 − fk]
f'''k =1/2h3[ fk+2 −2 fk+1 +2 fk−1 − fk−2]
Which formula do you find more accurate, and why?