Use the binomial expansion, in ascending powers of $x$, to show that
$$ ext{ } \sqrt{(4 - x)} = 2 - \frac{1}{4}x + kx^2 + ...$$
where $k$ is a rational constant to be found - Edexcel - A-Level Maths Pure - Question 9 - 2017 - Paper 2
Question 9
Use the binomial expansion, in ascending powers of $x$, to show that
$$ ext{ } \sqrt{(4 - x)} = 2 - \frac{1}{4}x + kx^2 + ...$$
where $k$ is a rational constant to... show full transcript
Worked Solution & Example Answer:Use the binomial expansion, in ascending powers of $x$, to show that
$$ ext{ } \sqrt{(4 - x)} = 2 - \frac{1}{4}x + kx^2 + ...$$
where $k$ is a rational constant to be found - Edexcel - A-Level Maths Pure - Question 9 - 2017 - Paper 2
Step 1
Use the binomial expansion to show that $\sqrt{(4 - x)} = 2 - \frac{1}{4}x + kx^2 + ...$
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Answer
To begin the expansion, factor out 4 from the square root: 4(1−4x)=2(1−4x)
Using the binomial expansion for (1+u)n, where u=−4x and n=21:
State, giving a reason, if the expansion is valid for this value of x.
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Answer
The expansion is valid for ∣x∣<4, so when substituting x=1, it is valid because ∣1∣<4. Thus, the approximation for 3 can be obtained using this expansion.
