The rupee appreciated 2 paise to 83.84 against the US dollar in early trade on Tuesday, helped by a weak greenback against major crosses overseas and lower crude oil prices in international markets. However, a sluggish trend in the domestic equities and fresh foreign fund outflows amid US rate cut expectations restricted the rise in the local unit, forex traders said. At the interbank foreign exchange market, the local unit opened slightly weak at 83.87 but gained some ground to turn positive at 83.84, registering a rise of 2 paise from its previous close. On Monday, the local unit settled at 83.86 against the US dollar. "A decline in crude oil prices, (recent) healthy foreign institutional inflows into Indian equities, and speculation about a possible rate cut by the Federal Reserve have stirred hopes of stability. Moreover, the Reserve Bank of India is poised to step in around the crucial 84-mark, likely deploying its reserves to prevent a further slide in the rupee," said, Amit