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微积分极限问题 求完整过程 可以的话 写在纸上 拍照 赶紧不尽

微积分极限问题 求完整过程 可以的话 写在纸上 拍照 赶紧不尽字迹工整些 怕看不懂

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Answer 1

(5)洛必达法则=lim(sec²x-1)/(1+cosx)=0/2=0
(7)等价无穷小=lim(sinx-1)/4(x-π/2)²
=limcosx/8(x-π/2)
=lim-sinx/8
=-1/8
(9)=lim(e^x+sinx-1)/sinx
=lim(e^x+cosx)/cosx
=2
(11)=limsinπx/2*lim(1-x)/cosπx/2
=1*lim-1/-(π/2)sinπx/2
=2/π
(13)=lim(-3cos3x/sin3x)/(-cosx/sinx)
=lim3sinx/sin3x*limcos3x/cosx
=lim3x/3x*1
(15)=e^limtanxln(1/x)
=e^lim-lnx/cotx
=e^lim(-1/x)/(-csc²x)
=e^limsin²x/x
=e^0
=1

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