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Define
f(x)=((e^x-1)²)/(sin(x/a) log(1+x/4)) for x≠ 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: 3
Solution
As x->0, (e^x-1)^2 ~ x^2 and sin(x/a)log(1+x/4) ~ (x/a)(x/4) = x^2/(4a), so the limit is 4a. Continuity needs 4a = 12, hence a = 3.
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