Question

Find the product of (t+n)x(3t+n), using horizontal method.​

Answer 1

Answer:

y=f({x}_{0})+{f}^{\prime }({x}_{0})(x-{x}_{0}).

Therefore, {x}_{1} must satisfy

f({x}_{0})+{f}^{\prime }({x}_{0})({x}_{1}-{x}_{0})=0.

Solving this equation for {x}_{1}, we conclude that

{x}_{1}={x}_{0}-\frac{f({x}_{0})}{f\prime ({x}_{0})}.

Similarly, the point ({x}_{2},0) is the x-intercept of the tangent line to f at {x}_{1}. Therefore, {x}_{2} satisfies the equation

{x}_{2}={x}_{1}-\frac{f({x}_{1})}{f\prime ({x}_{1})}.

In general, for n>0,{x}_{n} satisfies

{x}_{n}={x}_{n-1}-\frac{f({x}_{n-1})}{f\prime ({x}_{n-1})}.

Next we see how to make use of this technique to approximate the root of the polynomial f(x)={x}^{3}-3x+1.

Step-by-step explanation: