Let f(x)=x^2- 3. 1. show that [0, 2] is a bracketing interval for f 2. carry out 3 iterations of the bisection method applied to f with initial bracketing interval 0, 2]. give your estimate for the root and the error bound

root estimate = 1.75

error bound = 0.25

Step-by-step explanation:

f is a polynomial, so it is continuous in R (real numbers). Then you can use Bolzano's theorem.

f(0) = -3.1 < 0

f(2) = 4 - 3.1 = 0.9 > 0

Then there exists c in [0, 2], for which f(c) = 0

In the bisection method you generate a sequence of approximations of a root. If you have a bracketing interval [a, b], such that

f(a) and f(b) have opposite signs, then you use  approximate the root as

In this case:

Then:

The error bound is half the width of the interval [1.5, 2]

answer would be 8.64 or s = 11π/4 inches

step-by-step explanation:

s = r θ  

where s = arc length  

r = radius = 3 inches  

θ = central angle in radians = ( π /180)*165  

s = 3(π/180)*165  

= 8.64 inches