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Prove limit of (sin2x)/(2x) as x approached 0 is 1. By prove I mean using the epsilon/delta definition of precise limit. You may use the fact that the limit of (sinx)/x as x approaches 0 is 1.

attempt: (where E=epsilon and d=delta)

|(sin2x)/(2x) - 1| < E if |x|<d

2(-E+1) < (sin2x)/(2x) < 2(E+1)

...now im guessing that from here you need to isolate the x so as to get |x| is less than some expression, which solves for delta. But when I try this I keep getting that x is greater than some number, not less. Also I do not know what my professor means by being able to use the limit of sinx/x?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Prove limit of (sin2x)/(2x) as x approached 0 is 1?

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