Math CentralQuandaries & Queries


Question from pearl, a student:

(what is the value of limit of x as it approaches 0 of sin8x divided by cos6x)

Hi Pearl,

You know the limit of $\large \frac{\sin(t)}{t}$ as $t$ goes to 0 and the limit of $\large \frac{\cos(t)}{t}$ as $t$ goes to zero. For your expression


first write the numerator as

\[\sin(8x) = 8x \times \frac{\sin(8x)}{8x}.\]

Now do something similar for $\cos(6x).$ Put your original fraction


back together and simplify.


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