Let , a continuous function on with . Using interval halving that begins with , what…

MATHEMATICS · Single correct · A Level · Mathematics · Numerical methods · Numerical methods

Problem

Let

g(x)=x^{2}-5

, a continuous function on

[2,3]

with

g(2)<0

and

g(3)>0

. Using interval halving that begins with

[2,3]

, what is the midpoint approximation of the root after exactly two halvings? (a)

2.50

(b)

2.25

(c)

2.125

(d)

2.236