Determine limt→0t3tan32t
limt→0t3tan32t=limt→0t3sin32tcos32t=limt→0t3sin32t⋅cos32t⟸If we introduce 88 such that...limt→0t3tan32t=limt→08t3sin32t⋅cos32t8⟸we can rewrite the limit as...limt→0t3tan32t=limt→0(2tsin2t)3⋅cos32t8⟸recall that limt→0sintt=1limt→0t3tan32t=limt→0(1)3⋅limt→0cos32(0)8limt→0t3tan32t=1⋅18limt→0t3tan32t=18
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