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If the function f(x) = ( x) - ( x) x - x is continuous at x = 0, then f(0) is equal to .
2
For continuity, f(0) = x 0 f(x).
Expansions near x = 0:
x = x + x33 + , x = x - x36 +
( x) = x + 3 x3 + = x + x33 + x33 + = x + 2x33 +
( x) = x - 3 x6 + = x - x36 - x36 + = x - x33 +
numerator = x3 +
Denominator: x - x = x33 + x36 + = x32 +
f(0) = x 0 x3 x32 = 2
Answer: 2
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