The functions f and g are defined, for 0 x , by f(x) = e

The functions f and g are defined, for 0 ≤ x ≤ π, by f(x) = e^x−2 and g(x) = 5 − cos x.

The diagram shows the graph of y = f(x) and the graph of y = g(x).

The gradients of the curves are equal both when x = p and when x = q.

a. Given that p < q, verify by calculation that p is 0.16 correct to 2 decimal places.

b. Show that q satisfies the equation q = 2 + ln(sin q).

c. Given also that 1.5 < q < 2.5, use the iterative formula q_n+1= 2 + In(sin q_n)  to calculate q correct to 2 decimal places, showing the result of each iteration to 4 decimal places.

Transcribed Image Text:

y O y = 5-cos.x y = ex-2 X