Answer:
Step-by-step explanation:
Given that:
cos(x) = x³
f(x) = cos (x) - x³
f(x) is continuous on the interval (0, 1)
when;
f(0) = cos (0) - (0)
f(0) = 1 - 0
f(0) = 1 > 0
f(1) = cos (1) - 1³
f(1) = 0.5403 - 1
f(1) = -0.4597
f(1) = - 0.46
f(1) = - 0.46 < 0
Since, 1 > 0 > -0.46, thus there is a number ''c" in (0,1)
such that f(c) = 0
By applying the Intermediate Value Theorem, there is a root of the equation in the interval (0,1)
b) Given that:
The interval length = 0.01; this implies that it is 0.005 length from its root.
f(0.865) = 0.0014
f(0.87) = - 0.013
The solution to the interval lies between 0.865 , 0.87 by using a calculator at length 0.01.
