limX→0+ (lnX-2/π)/cotX求极限

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limX→0+ (lnX-2/π)/cotX求极限

limX→0+ (lnX-2/π)/cotX求极限
limX→0+ (lnX-2/π)/cotX求极限

limX→0+ (lnX-2/π)/cotX求极限
lim(X→0+) (lnX-2/π)/cotX
=lim(X→0+)(1/X)/(-csc²x) 【洛必达法则】
=lim(X→0+)(1/X)/(-1/sin²X)
=lim(X→0+)-(sin²X)/X
=lim(X→0+)-sinX 【上步等价无穷大代换,X→0时,sinX】
=0
答案:0

L'Hopital法则
lim (lnx-2/pi)/cotx = lim (1/x)/(-csc^2 x) = lim (-sin^2 x)/x = 0

原式=
lim (lnx-2/pi)/cotx
=lim (1/x)/-(cscx)^2
=lim -(sinx)^2/x
=lim -x^2/x
=lim-x
=0