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How do I evaluate the limit sin9x divided by tan9x when x tends to 0 without using L Hospitals rule?
Wiki User
∙ 14y ago
First to simplify matters, change y=9x. So we are looking at limit sin(y) divided by tan(y).
Now lets look at right angled triangle where
sin(y) = a/c
tan(y) = a/b
thus we are looking at the limit of (a/c)/(a/b) = limit of b/c
As the angle y shrinks, the right angle remains constant, and the remaining angle approaches a right angle. Thus at the limit we have a triangle with equal angles and thus where b=c.
As a result limit you are trying to calculate is 1.
Wiki User
∙ 14y ago
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