Final answer:
In this scenario, sending positive confirmation requests would be the most appropriate method to determine the existence of accounts receivable balances.
Step-by-step explanation:
In this scenario, where all receivable balances are small, customers are billed monthly, and internal control is effective, the most appropriate method for Smith to determine the existence of accounts receivable balances at the balance sheet date would be to send positive confirmation requests. Positive confirmation requests are sent directly to customers asking them to confirm the amount of their outstanding balances. This method provides direct and reliable evidence of the existence of the accounts receivable balances.