Question

Find a root of an equation f(x)=sinx−ex+2 using the interval (0, 2) and correct up to 4 decimal place

Answer 1

Explanation:

The Newton-Raphson method is a iterative method to find roots. It requires a function set to zero and its first derivative.

xn+1=xn−f(x)f′(x)

f(x)=xsin(x)+cos(x) function set to zero

f′(x)=xcos(x)+cos(x)−sin(x) first derivative

xn+1=xn−xnsin(xn)+cos(xn)xncos(xn)+cos(xn)−sin(xn)