f(x) = x3 - 2x - 5
(a) Show that the equation f(x) = 0 has a root α between x = 2 and x = 3.
(b) Using x0 = 2, apply the Newton–Raphson method twice to find x2, giving your answer to 4 decimal places.
(c) Explain why the Newton–Raphson method would fail with x0 = √(2/3).
From Paper 2: Pure and Mechanics
79 marks
(a) The curve y = x2 - 4x + 5 and the line y = x + 1 intersect at two points. Find the exact area of the region enclosed between them.
(b) Use the trapezium rule with 4 strips to estimate ∫02 √(1 + x3) dx, and state whether your answer is an overestimate or an underestimate, giving a reason.
Score 0 / 16 · 0 of 2 marked
This paper is written by Plasmo in the style of the AQA A-Level Maths exam. It is not a past paper and is not produced or endorsed by the exam board.