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Yes, you can use the visa to apply for entry into the United States up to and including the day of its expiration. This is regulated at 22 CFR 41.112(a):
Β§ 41.112 Validity of visa.
(a) Significance of period of validity of visa.
The period of validity of a nonimmigrant visa is the period during which the alien may use it in making application for admission. The period of visa validity has no relation to the period of time the immigration authorities at a port of entry may authorize the alien to stay in the United States.