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Answer :
Final answer:
The limit lim x->0 sin6x/3x is equal to 1/3.
Explanation:
To find the limit lim x->0 sin6x/3x, we can use the given fact lim ∅->0 sin∅/∅ =1 and apply it to our problem.
First, we can rewrite sin6x/3x as (sin6x)/(6x) * (6x)/(3x). Now, we can see that the first term sin6x/6x is equivalent to sin(6x)/6x, and the second term 6x/3x simplifies to 2.
So, we have (sin(6x)/6x) * 2. Now, we can apply the given fact lim ∅->0 sin∅/∅ =1 to the first term sin(6x)/6x. As x approaches 0, 6x approaches 0, so we can substitute ∅ = 6x into the given fact.
Therefore, the limit lim x->0 sin6x/3x is equal to (sin(6x)/6x) * 2 = (1/6) * 2 = 1/3.
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