Question

We wish to solve x2 - 2 = 0 by Newton Raphson technique. If initial guess is x0 = 1.0, subsequent estimate of x (i.e. x1) will be

Answer 1

Answer:

$\mathbb \red {CALCULATION} : \\ \green{Given:} \\ {x}^{2}  - 2 = 0 \\ f(x) =  {x}^{2} - 2 ⇒ f'(x) = 2x \\ ∴ \: At \: n=0⇒x_{1} =x_{0}− \frac{f(x_{0})}{f′(x_{0})} \\ x_{0}=1 \\ f(1)= {1}^{2} −2=−1 \\ f′(1)=2 \\ ∴ x_{1} =1− \frac{ (- 1)}{2} =1.5 \\ ∴ Value \: of \: Iteration \: after \\ {1}^{st}   \: iteration = 1.5 \\ \purple{\rule{45pt}{7pt}}\red{\rule{45pt}{7pt}}\pink{\rule{45pt}{7pt}}\blue{\rule{45pt}{7pt}}$