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Math Help - Limits involving trig

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    Limits involving trig

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    Senior Member apcalculus's Avatar
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    Quote Originally Posted by janedoe View Post
    They multiplied by 1/2 and divided by 1/2.

    In the last step they used the fact that \frac{sin x}{x} goes to 1 and x goes to 0.
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    Quote Originally Posted by apcalculus View Post
    They multiplied by 1/2 and divided by 1/2.

    In the last step they used the fact that \frac{sin x}{x} goes to 1 and x goes to 0.

    I'm sorry, I'm still not getting it =[ You mean, multiply the whole thing by 1/2, and then divide vy half as in, multiply by 2/1 ?
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    Senior Member apcalculus's Avatar
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    Quote Originally Posted by janedoe View Post
    I'm sorry, I'm still not getting it =[ You mean, multiply the whole thing by 1/2, and then divide vy half as in, multiply by 2/1 ?

    If you have a fraction like \frac{m}{n} , it is the same as

    \frac{1*m}{0.5*\frac{n}{0.5}}

    Now split into a product of fractions and write the 0.5 and \frac{1}{2}, to get:

    \frac{1}{\frac{1}{2}} \frac{m}{\frac{n}{\frac{1}{2}}}

    Note that \frac{1}{\frac{1}{2}} is 2 and can be pulled in front of the limit sign since it is a constant.

    That's all we're doing. I hope this helps.
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