Question

Use the intermediate value theorem and a graphing utility to approximate the zero of the function in the interval [0, 1].Repeatedly " zoom in" on the graph of the function to approximate the zero accurate to two decimal places. Use the zero or root feature of the graphing utility to approximate the zero accurate to four decimal places.

g (t) = 2 cos t - 3t

Answer 1

Step 1 :

The function is in the interval .

It follows that , apply intermediate value theorem to conclude that there must be some in such that .

Step 2 :

Find out zero value using  graphing utility :

From the above graph the zero value is nearly , it is located between and .

Step 3:

To find out the accurate value of value, need to zoom the graphing utility as shown below.

We clearly observe from the above graph the zero value is nearly .

Solution:

The zero value approximated to two decimal points is .

The zero value approximated to four decimal points is .