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(Cos2x+sin3x)∧Cot5x的极限

原式=lim(x->0) {[1+(cos2x+sin3x-1)]^[1/(cos2x+sin3x-1)]}^[(cos2x+sin3x-1)/tan5x] =e^lim(x->0) [(cos2x+sin3x-1)/tan5x] =e^lim(x->0) [(cos2x+sin3x-1)/(5x)] =e^lim(x->0) (-2sin2x+3cos3x)/5 =e^(3/5)

=lime^(cos5x/sin5x*ln(cos2x+sin3x)) =lime^(cos5x/sin5x*sin3x) =e^(3/5)

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