(a) Show that the equation f (x) = 0 has a solution in the interval 0.8 <x< 0.9
The curve with equation y = f (x) has a minimum point P.
(b) Show that the x-coordinate of P is the solution of the equation
x = [3 + sin(½ x)]/2
(c) Using the iteration formula
xn+1 = [3 + sin(½ xn)]/2 , x0 = 2
find the values of x1, x2 and x3 , giving your answers to 3 decimal places.
(d) By choosing a suitable interval, show that the x-coordinate of P is 1.9078 correct to 4 decimal places.
6 (a) Roots - Change of sign method.
(b) Find f-1(x)
(c) Find the domain of f−1
g(x) = ln(x + 1)
(d) Find the solution of fg(x) = 1/7, giving your answer in terms of e.7 (a) Simplifying algebraic fractions.
8. (a) Starting from the formulae for sin ( A + B ) and cos ( A + B ), prove that
tan (A + B) = (tan A + tan B)/(1 - tanA tanB)
(b) Deduce that
(c) Hence, or otherwise, solve, for 0 ≤ θ ≤ π ,
1 + √3 tanθ = (√3 - tanθ)tan(π - θ)
Give your answers as multiples of π8 (a) Trig. Identities
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.