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]

12*c

step-by-step explanation:

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is