用洛必达法则,求极限,谢谢
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⑴、原式=limx→0 [(1/cos2x)*(-sin2x)*2]/[(1/(cos3x)*(-sin3x)*3]
=limx→0 2sin2x/3sin3x,
=limx→0 2sin2x*2/3cos3x*3,
=4/9;
⑵、原式=limt→0 [t-ln(1+t)]/tln(1+t),
=limt→0 [t-ln(1+t)]/t^2,
=limt→0 [1-1/(1+t)]/2t,
=limt→0 1/2(1+t),
=1/2;
⑶、原式=e^limx→0+ xln(ln1/x)
=e^limt→∞ ln(lnt)/t,
=e^limt→∞ (1/t)/lnt,
=e^0
=1。
=limx→0 2sin2x/3sin3x,
=limx→0 2sin2x*2/3cos3x*3,
=4/9;
⑵、原式=limt→0 [t-ln(1+t)]/tln(1+t),
=limt→0 [t-ln(1+t)]/t^2,
=limt→0 [1-1/(1+t)]/2t,
=limt→0 1/2(1+t),
=1/2;
⑶、原式=e^limx→0+ xln(ln1/x)
=e^limt→∞ ln(lnt)/t,
=e^limt→∞ (1/t)/lnt,
=e^0
=1。
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