Use the bisection method to find √ 2 correct to roughly within 10^−2 . (hint: consider f(x) = x^2 − 2 on [1, 2])

Using the Bisection Method

Step-by-step explanation:

These are the steps for the Bisection Method:

Suppose we need a root for f(x) = 0 and we have an error tolerance of ε

We know from the information given that

Applying the steps of the Bisection Method you get:

1. There is a root between [1,2] because:

2. Define

3.

4. Because we set 1.5 as the new b.

The bisection algorithm is detailed in the following table.

Note that after 7 steps we have hence the required root approximation is c = 1.4106

correct answers below:

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!