0.707 … 0.30.3 = 0.696 … 0.10.1 = 0.794 … 0.010.01 = 0.954 … 0.0010.001 = 0.993 … lim 𝑥𝑥→0+ 𝑥𝑥𝑥𝑥 = 1 lim 𝑥𝑥→0 𝑥𝑥𝑥𝑥 = lim 𝑥𝑥→0 𝑒𝑒ln(𝑥𝑥)𝑥𝑥 lim 𝑥𝑥→0 𝑥𝑥𝑥𝑥 = 𝑒𝑒lim 𝑥𝑥→0 ln(𝑥𝑥)×𝑥𝑥 lim 𝑥𝑥→0 𝑥𝑥𝑥𝑥 = 𝑒𝑒lim 𝑥𝑥→0 ln 𝑥𝑥 𝑥𝑥−1 lim 𝑥𝑥→0 𝑥𝑥𝑥𝑥 = 𝑒𝑒 lim 𝑥𝑥→0 𝑑𝑑 𝑑𝑑𝑑𝑑ln 𝑥𝑥 𝑑𝑑 𝑑𝑑𝑑𝑑𝑥𝑥−1 lim 𝑥𝑥→0 𝑥𝑥𝑥𝑥 = 𝑒𝑒lim 𝑥𝑥→0 𝑥𝑥−1 −𝑥𝑥−2 lim 𝑥𝑥→0 𝑥𝑥𝑥𝑥 = 𝑒𝑒lim 𝑥𝑥→0 𝑥𝑥 lim 𝑥𝑥→0 𝑥𝑥𝑥𝑥 = 𝑒𝑒0 lim 𝑥𝑥→0 𝑥𝑥𝑥𝑥 = 1