lim sin 2x / sin 5x lim arctan x / xx趋近于0 x趋近于0
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limsin2x/sin5xlimarctanx/xx趋近于0x趋近于0limsin2x/sin5xlimarctanx/xx趋近于0x趋近于0limsin2x/sin5xlimarctanx/xx趋
lim sin 2x / sin 5x lim arctan x / xx趋近于0 x趋近于0
lim sin 2x / sin 5x lim arctan x / x
x趋近于0 x趋近于0
lim sin 2x / sin 5x lim arctan x / xx趋近于0 x趋近于0
(1) sin2x 5x sin2x 2
lim -------------------=lim--------------*lim------------ *------ =2/5
x→0 sin 5x x→0 sin 5x x→0 2x 5
(2) arctanx (arctanx)' 1/(1+x²)
lim -------------=lim ------------------ =lim-----------------=1
x→0 x x→0 (x)' x→0 1
解析:2/5 1
lim sin2x/sin5x=lim(sin2x/2x)*(sin5x/5)* 2/5 =2/5
运用罗比达法则 上下代数式都趋近于0时 同时求导 limarctanx / x=lim1/(1+x^2)
所以 当 x趋近于0时 等于1
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