a. By sketching each of the graphs of = sec y x and

on the same diagram, show that the equation

has exactly two real roots in the interval

b. Show that the equation

can be written in the form

c. The two real roots of the equation

in the interval

are denoted α and β.

Verify by calculation that the smaller root, α, is −0.21 correct to 2 decimal places.

d. Using an iterative formula based on the equation given in part b, with an initial value of 1, find the value of β correct to 2 decimal places. Give the result of each iteration to 4 decimal places.

Transcribed Image Text:

x = (1 - x)( + + x) for - 1 < x < y 1/ 2 2 2