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## Homework Statement

g(x) = 1 if x is rational, 0 if x is irrational.

Determine the limit, or prove it doesn't exist.

lim g(x)sinx

x->0

## Homework Equations

## The Attempt at a Solution

I said the limit is 0.

0 < |g(x)sinx| < |sinx|

lim |g(x)sinx|= 0

x->0

-|sinx| < g(x)sinx < sinx

lim g(x)sinx

x->0

The < are less than or equal. I can't figure out how to put them in correctly.

This was on my final and it's driving me crazy! I couldn't decided if the limit was 0 or didn't exist. If you could point out my mistakes I'd appreciate it!