Calculus/limits

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Expert: - 5/13/2010


Question
how do you find the lim as x approaches 0 of (sin5x/3x)?
Thanks, Michelle

Answer
It is known that lim(x->0) (sinx/x) = 1.

Since we have sin(5x), we need a 5x on the bottom.

The way to do this is multiply by (5/3)/(5/3).

This gives (5/3)sin(5x)/(5x).

Let z=5x, and so we have (5/3)sinz/z.

As x->0, z->0.

We now have (5/3)lim(z->0)(sinz/z).

Note the limit was given in the first line, so multiply the value of the limit by 5/3.

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