Starting from an initial interval (2, 3) containing 5, we will simply take the midpoint of...

Transcribed Image Text:

Starting from an initial interval (2, 3) containing √5, we will simply take the midpoint of the interval and determine whether √5 is contained in which of the two subintervals divided by the midpoint, i.e., whether √5 is greater or less than the midpoint . For instance, let's call b₁ = 2 be the first approximation and b₂ = 2.5 be the second approximation determined by the midpoint of 2 and 3. Since 2<√5 <2.5, the third approximation b3 should be determined by the midpoint of (2,2.5). iii) Provide b3, b4 and the corresponding error bounds €3, €4. iv) Provide the error bounds en corresponding to the nth approximation b Starting from an initial interval (2, 3) containing √5, we will simply take the midpoint of the interval and determine whether √5 is contained in which of the two subintervals divided by the midpoint, i.e., whether √5 is greater or less than the midpoint . For instance, let's call b₁ = 2 be the first approximation and b₂ = 2.5 be the second approximation determined by the midpoint of 2 and 3. Since 2<√5 <2.5, the third approximation b3 should be determined by the midpoint of (2,2.5). iii) Provide b3, b4 and the corresponding error bounds €3, €4. iv) Provide the error bounds en corresponding to the nth approximation b

Answer rating: 100% (QA)

Using the method described we have b 2 b 232 25 Since 2 5 25 we take the midpoint of 2 25 as the nex... View the full answer