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Define f(x)=((e^x-1)^2)/(sin(x/a)\,\log(1+x/4)) for x\ne 0, and set f(0)=12. If f is continuous at x=0, what is the value of a?
- 1
- -1
- 2
- 3
Correct answer: -1
Solution
To ensure continuity at x=0, the limit of f(x) as x approaches 0 must equal f(0). Evaluating the limit leads to the requirement that the expression simplifies to 12 when substituting a = -1, thus making the function continuous at that point.
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