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Sed (CoderLovesEggs) Paper 1 with Solutions · Q20

Paper 1Functions & graphs

For all integers n≥1n\ge1, define the function f(x)f(x) as

f(x)=(−1)n+122−2n−(x−4+62n)2f(x)=(-1)^{n+1}\sqrt{2^{2-2n}-\left(x-4+\frac6{2^n}\right)^2}

for 4−23−n≤x<4−22−n4-2^{3-n}\le x<4-2^{2-n} only.

It follows that the total length of the curve f(x)f(x) is:

A3π5\dfrac{3\pi}5;
B2π3\dfrac{2\pi}3;
C3π2\dfrac{3\pi}2;
Dπ\pi;
E2π2\pi;
F4π4\pi;
G44.

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