求极限lim(1/x2-1/(xtanx)) x→0

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求极限lim(1/x2-1/(xtanx)) x→0

求极限lim(1/x2-1/(xtanx)) x→0
求极限lim(1/x2-1/(xtanx)) x→0

求极限lim(1/x2-1/(xtanx)) x→0
lim (1/x^2 - 1/xtanx)
= lim(xtanx - x^2)/(x^3 * tanx) 约去一个tanx
= lim (tanx - x)/x^3 上下都求导数(罗必达法则)
= lim (secx * secx -1)/3x^2
= lim (tanx * tanx)/3x^2
= 1/3

=lim[tanx-x]/x^3=lim[sec^2x-1]/3x^2=lim2sec^2xtanx/6x=1/3