| Exam Board | AQA |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2012 |
| Session | January |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Approximation for small x |
| Difficulty | Standard +0.3 This is a straightforward application of binomial expansion for small x to evaluate an indeterminate limit. Students need to expand √(4+x) = 2(1+x/4)^(1/2) using the binomial theorem, substitute into the expression, and simplify. While it requires recognizing the technique and careful algebra, it's a standard FP3 exercise with no novel insight required—slightly easier than average for Further Maths. |
| Spec | 4.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n |
2 Find
$$\lim _ { x \rightarrow 0 } \left[ \frac { \sqrt { 4 + x } - 2 } { x + x ^ { 2 } } \right]$$
(3 marks)
\hfill \mbox{\textit{AQA FP3 2012 Q2 [3]}}