The expansion of \({(9\;-\;4x^2)}^\frac12\) is valid for
- \(-\frac12\leq x\;\leq1\)
- \(-2\leq x\;\leq\frac12\)
- \(-\frac13\leq x\;\leq\frac13\)
- \(-\frac32\leq x\;\leq\frac32\)
2 Answers
\({(9\;-\;4x^2)}^\frac12\)
= \(3\left(1-\frac{4x^2}9\right)^\frac12\)
This is valid if \(\frac{4x^2}9<1\)
Or, \(x^2<\frac94\;or,\;\left|x\right|<\frac32\;\)
∴ \(-\frac32\leq x\;\leq\frac32\)
-3/2<x<3/2
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