Evaluate lim_{sin 3 theta sin 7 theta}/{ heta^2}.
theta -- 0
find limit

Question

Evaluate lim_{sin 3 theta sin 7 theta}/{	heta^2}.
theta --> 0 
find limit

psymon · Answer

$$\frac{ (\sin3 \theta)(\sin7 \theta) }{ (\theta)^{2} }$$
Correct?

anonymous · Answer

yes

psymon · Answer

Okay, so the main identity we want to know is 
$$\lim_{x \rightarrow 0}\frac{ sinx }{ x }=1$$Doesnt really matter what x is for the most part, as long as you have the same value in the angle of sin as you do in the denominator. So right now you have a 3theta and a 7 theta on top, but only 2 thetas on bottom. So we're missing a 3 to cancel out one sin and a 7 to cancel out another. SO what we need to do is multiply a 3 and a 7 in there. This can be done by multiply both top and bottom by 7 as well as top and bottom by 3 at the same time. That way we can sneak a 3 and a 7 in the denominator to take advantage of our identity. 


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