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The function f: R - {0} → R given by f(x) = 1/x - 2/(e^(2x) - 1) can be made continuous at x = 0 by defining f(0) as

1. 0
2. 1
3. 2
4. 4

Correct answer: 1

Solution

Combine to [(e^(2x)-1)-2x]/[x(e^(2x)-1)]. With e^(2x)-1 = 2x+2x^2+(4/3)x^3+..., numerator = 2x^2+(4/3)x^3, denominator = 2x^2+2x^3, so the limit as x->0 is 1. Define f(0)=1.

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